Roast the pumpkin: Open the pumpkin with a bread knife, spoon out the seeds and innards and remove them. Chop the pumpkin into slices, peel the skin off (with a potato peeler or a knife if too thick) and arrange on a baking tray. Drizzle with olive oil, add some salt and put in the oven at 180 °C (fan). Let it cook until the flesh turns very soft and the outside is barely beginning to char around the edges; it usually takes around 20-30 minutes but I find that it really varies a lot between different pumpkins, so just check from time to time. Let it cool down and set aside the amount you are going to need for the recipe; you can divide into portions and freeze the rest to use in other preparations.
Cook the mushrooms: Cut out any parts of the mushrooms that have excessive dirt or that do not look fresh. Wash the mushrooms gently with a wet cloth - do not wash them under a running tap and absolutely do not soak them as they will turn spongey and full of liquid. Chop the mushrooms into small pieces. Add a little olive oil to a pan, turn the heat on to medium and add a clove of garlic split in half. When bubbles form in the oil around the garlic, add the mushrooms to the pan (if the mushrooms have different textures you can add them in stages; e.g. I added the king oysters first because their flesh is tougher). Do not add salt at this stage or the mushrooms will start leaking water out. Let them cook gently, stirring from time to time, until soft and fragrant. Wash the parsley, remove the stalks and chop finely. Once the mushrooms are ready discard the garlic, add salt and pepper to taste and stir in the chopped parsley. Set aside.
Pre-cook the pasta shells: Bring a pot of water to boil, salt it and toss in the conchiglioni. Let them cook for 5 minutes (or follow the instructions on the package if different), stirring from time to time, and then remove from the pot and let them cool down. Discard the ones that are too badly broken. Do not throw away the water, or at least keep some aside for the pumpkin sauce.
Prepare the pumpkin sauce: Add a little olive oil to a pan on medium heat, a garlic clove sliced in halves and the tomato concentrate. Keep stirring until fragrant and then add the pumpkin flesh. Let it heat up a little and then add a ladle of the water you cooked the pasta in. Fold it in and add more water until the mixture has the texture of thick soup. Let it cook for about 10 minutes, during which it will become somewhat thicker. Keep stirring because pumpkin has a tendency to stick and thus burn. Once the sauce is ready (and not too thick - add more water if needed, one tablespoon at a time), remove the garlic and adjust the salt if needed. Line the baking tray with baking paper and transfer the pumpkin sauce to the lined tray, spreading so as to make a uniform layer on the bottom.
Stuff the pasta shells: Chop half of the prosciutto cotto into little squares and chop the rest very finely - almost to a paste. In a large bowl add the chopped prosciutto cotto, the ricotta, the cooked mushrooms and 50 gr of grated parmigiano cheese. Mix well, taste and add a pinch of salt if needed. Stuff the conchiglioni with the help of a spoon, trying to divide the filling evenly between the shells. Transfer the shells to the tray, resting them on the pumpkin sauce with the open side facing upwards.
Make the bechamel sauce: Add the butter to a non-stick pan and set the heat to medium-low (2 marks out of 6 on my cooking unit). After it melts it will start making bubbles: mix gently but let it bubble all the way, until no more bubbles form. This is to remove the water from the butter and greatly reduce the chance of clumps forming. At this point you can add the flour, all in one go, and mix it well with the butter (a scraper works well for this). It will have the thickness of toothpaste; this mixture is called a roux. Let it cook on medium-low (or medium, if you pay close attention to it), stirring regularly. After a few minutes you will witness a very noticeable change in the thickness of the roux, as it will become a lot thinner and more liquid-like (this happens rapidly, over the course of a minute or so). Now the roux is ready to take in the milk. Pour all the milk (cold from the fridge) in the pan and mix gently with the roux using a whisk. Be careful not to ruin the non-stick coating with the whisk; they make whisks which are coated in rubber, those are safe. Turn the heat up to medium and let the milk heat up slowly, stirring regularly. Add a generous amount of salt and grate some nutmeg. Once the mixture approaches the boiling point the gelification will start and your bechamel sauce will come together, becoming thick and smooth. Turn down the heat to the lowest setting, cover with a lid and let it cook for at least 20 minutes, stirring from time to time. After this time has passed, taste it and adjust the salt. If it still tastes a little like raw flour, let it cook 10 more minutes, or as long as needed; if it gets too thick, just add a dash of milk and fold it in. This recipe guarantees no clumps if followed correctly, but if for some reason you find clumps in your sauce you can get rid of them with an immersion blender. Let the sauce cook some more after the blending, to get rid of the raw flour taste.
Bake: Pour the bechamel sauce over the conchiglioni, spreading it with a spoon to make sure that they are evenly covered. Grate some parmigiano cheese (or pecorino) on top and move to the oven. Set the temperature to 180 °C (fan) and let it bake for 20 minutes. After this time has passed, check the degree of crispiness of the top of the dish and continue cooking until it is to your liking (raising the oven temperature). Remove from the oven and let it rest for 5 minutes.
Plate and serve.