In a large pot of salted boiling water, cook the pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Remove the sausage from its casing and add to the skillet. Cook, breaking it up with a wooden spoon, until browned and cooked through (about 5-7 minutes). Remove and set aside.
In the same skillet, add the Brussels sprouts and butternut squash. Sauté for about 5-6 minutes until they begin to soften. Add the minced garlic, red pepper flakes, and thyme. Cook for another 2-3 minutes until fragrant.
Add the cooked sausage back to the skillet, then pour in the vegetable broth. Bring to a simmer and cook for 2-3 minutes, allowing the flavors to meld.
Stir in the cooked pasta and Parmesan cheese until well combined. If the mixture seems dry, add an extra splash of vegetable broth. Season with salt and pepper to taste.
Divide the pasta among plates, garnishing with fresh parsley and additional Parmesan if desired.
Notes
Feel free to substitute with vegan sausage for a plant-based option.