Preheat the oven to 425°F (220°C). Line a rimmed baking sheet with parchment paper or foil and set aside.

Toss the butternut squash cubes with 1 teaspoon olive oil and a pinch of salt on one side of the baking sheet so they have room to roast rather than steam. Spread the halved Brussels sprouts on the other side of the sheet, drizzle with the remaining 1 teaspoon olive oil, and season with salt and pepper.

Roast squash and Brussels sprouts until tender and caramelized at the edges, about 20–25 minutes, turning once halfway through so both sides develop color. Remove from oven and keep warm.

Bring a large pot of salted water to a rolling boil and cook the farfalle until al dente according to package directions, usually 10–12 minutes. Reserve 1 cup of pasta cooking water, then drain the pasta.

While the pasta cooks, heat a large skillet over medium-high heat. Add 1 tablespoon olive oil and 1 tablespoon butter. Crumble the sausage into the skillet (or slice into medallions if you prefer) and cook until well browned with some seared crust, about 6–8 minutes. Break up larger pieces so you have a mix of small crumbles and bite-sized medallions. Transfer the cooked sausage to a bowl, leaving rendered fat in the skillet.

Reduce the heat to medium. Add the chopped shallot to the skillet and sauté in the sausage fat until translucent, 2–3 minutes. Add the minced garlic and cook 30–45 seconds until fragrant but not browned.

Pour in the chicken broth and heavy cream, stirring to deglaze the pan and lift flavorful browned bits from the bottom. Bring to a gentle simmer, then add the grated Parmesan cheese and stir until the sauce thickens slightly, 2–3 minutes. If the sauce becomes too thick, loosen it with some reserved pasta water, 1–2 tablespoons at a time.

Return the cooked sausage to the skillet along with the roasted squash and Brussels sprouts. Fold gently so squash cubes don’t fall apart, and heat through for 2–3 minutes so flavors marry. Taste and adjust seasoning with salt, pepper and red pepper flakes if using.

Add the drained farfalle to the skillet and toss everything together, adding up to 1/2 cup reserved pasta water if needed to achieve a glossy, clingy sauce that coats the pasta. Stir in the fresh thyme leaves and lemon zest.

Remove from heat and finish with chopped parsley and an extra grating of Parmesan. If desired, drizzle a little balsamic glaze over individual bowls for a subtle sweet-acid contrast. Garnish with whole thyme sprigs and serve immediately with additional black pepper.