Set the dough aside and let rest for 30 minutes.
Cut the dough into thirds and transfer to a floured work surface. Roll out as thinly as you can; flour is your friend here. Sprinkle a little flour on one part of the dough, roll it up into a tube like you would with a jelly roll, and cut it into strips. Repeat with the remaining dough, flouring the noodles generously to prevent sticking. The noodles can be refrigerated for up to 2 days before use.
For the sauce: Bring a large stock pot of salted water to a boil over high heat. Heat some olive oil in a large saucepan over medium-high heat. Add the mushrooms, Brussels sprouts and red peppers and cook until lightly caramelized. Turn the heat to low and add the cream, garlic and some salt and black pepper.
When the water has reached a rolling boil, drop your noodles into the pot and cook for 4 to 5 minutes. Transfer the noodles into the sauce using a spider strainer, adding 1 cup pasta cooking water, and then turn the heat to medium-high. (If you don't have a spider strainer, add 1 cup of pasta water to the sauce, and then separately drain and add the noodles without rinsing.) Cook the noodles in the sauce, stirring, until it all comes together and thickens, 2 to 3 minutes. Plate it up and finish the dish with some fresh lemon zest over top!