In large, wide pan or deep skillet with a tight-fitting lid, brown and crumble the sausage in olive oil over medium-high heat. Add onion, fennel, garlic, chili pepper, salt, pepper and thyme. Cover pan and cook to soften, 8-10 minutes, stirring occasionally. Uncover, stir in tomato paste and add vermouth and stock. Bring to a bubble, add pasta, cover and cook 7-8 minutes, tossing with tongs occasionally. If the pasta is sticking to the bottom of the pan, loosen the pasta with water.
Add mussels, cover and cook 3-4 minutes more to al dente, adding more stock or water if needed. Add parsley and adjust salt and pepper to taste. Serve directly from pan at the table.