Garganelli with Sausage and Mushroom Ragu

Name: Garganelli with Sausage and Mushroom Ragu
Ingredients: 10 cremini mushrooms, stems removed and reserved, caps sliced; 2 ribs celery, large dice; 2 carrots, peeled and large dice; 1 onion, large dice; 3 cloves garlic, peeled; Extra-virgin olive oil; Kosher salt; Pinch of crushed red pepper flakes; 1/2 pound sweet Italian sausage, casing removed; 1/2 pound spicy Italian sausage, casing removed; 1 cup red wine; 2 tablespoons tomato paste; 4 cups chicken stock; 4 to 5 sprigs thyme, tied with twine; 2 bay leaves; 1/2 cup freshly grated parmesan cheese, plus more for garnish; 1/2 cup fresh ricotta cheese; 1 pound all-purpose flour (about 3 1/3 cups), plus more for dusting; 4 large eggs plus 1 egg yolk; 1/4 cup extra-virgin olive oil; 1 teaspoon kosher salt; 1 to 2 tablespoons water, plus more as needed; Semolina flour, for the tray