Let's start from fresh pasta. Mix together the two flours and pour them onto a large cutting board. Add salt and knead with your hands adding water at room temperature as required to obtain a homogeneous and elastic dough. Let the dough rest on the board, covered with a cloth or a bowl, for at least half an hour.
Let's now prepare the cabbage and musrooms sauce. Heat a pan with chopped garlic, a drizzle of olive oil and a bit of water. When the garlic begins to brown add the mushrooms (chopped) and cook them halfway, on a medium heat.
Meanwhile wash the cabbage and cut it into strips about half an inch wide; add them to the mushrooms, season with salt and pepper, put the heat to low and cover with a lid.
While the cabbage is cooking, bring to a boil some slightly salted water in a pot (you'll need it for cooking pasta).
Roll out the chestnut dough with a rolling pin to the thickness you prefer; I like it quite thick (about 2 mm), but if you like it to be thinner you can roll it out a bit more. As you proceed add a little flour on the board, the dough and the rolling pin so that rolling out would be easier.
Now form a pasta roll about 4-5 cm wide. Cut it out into half cm wide strips and unroll with your hands the strips thus obtained...here are your chestnut tagliatelle :)
Now the cabbage should be done, so turn off the heat.
Even the water to cook the pasta should have reached the boil, so dip the tagliatelle into it gently. As soon as they come up to water surface drain them and pour them in the pan along with the cabbage and mushrooms sauce.
Sauté the tagliatelle with their sauce over low heat, add some pasta cooking water and stir for a few seconds before serving.
Serve the tagliatelle with a drizzle of good olive oil and, if you like, top with some Parmesan cheese (I prefer the vegan substitutes, such as nutritional yeast flakes and almond flour, or just almond flour).