1. Preheat the Oven and Line the Pan Set your oven to 425°F and position a rack in the center. Line a large rimmed baking sheet with parchment paper so the vegetables can brown without sticking and cleanup stays easy. Choose a pan with raised edges, since the vegetables will release some moisture and oil as they roast.

2. Cut the Sausage If your sausage is in long links, slice it into thick pieces or rounds, depending on the shape you prefer. To create the Hasselback look, use a sharp knife to make several shallow cuts across the top of each sausage piece, spacing the cuts a small distance apart. Take care not to slice all the way through, since the pieces need to stay intact. As the sausage roasts, those cuts will open up and the edges will brown and crisp.

3. Season the Vegetables Place the cubed butternut squash and halved Brussels sprouts directly on the lined baking sheet. Drizzle the olive oil over the top, then sprinkle on the salt, black pepper, garlic powder, smoked paprika, and dried thyme. Toss everything together with your hands or two large spoons until each piece is lightly coated in oil and seasoning, then spread the vegetables into a single, even layer. Leave a little space between pieces so they roast instead of steaming.

4. Add the Sausage Nestle the cut sausage pieces in among the vegetables, placing them cut-side up so the slits stay open and exposed to the heat. Make sure the sausage touches the pan in several spots so it browns well.

5. Roast Slide the pan into the preheated oven and roast for 25 to 30 minutes. Halfway through the cooking time, remove the pan and stir the vegetables so they brown evenly, then return it to the oven. The dinner is ready when the butternut squash is tender when pierced with a fork, the Brussels sprouts have browned edges, and the sausage is hot throughout with lightly crisped edges around the cuts.

6. Broil for Extra Color (Optional) For deeper browning, switch the oven to broil and place the pan under the heat for 1 to 2 minutes. Stay close and watch it carefully, since sprouts and sausage edges can go from golden to burnt in seconds.

7. Soften the Shallot While the sheet pan roasts, set a small saucepan over medium heat and add the butter. Once it melts and begins to foam, add the finely minced shallot. Cook for 2 to 3 minutes, stirring occasionally, until the shallot turns soft and translucent.

8. Add the Garlic, Thyme, and Liquids Stir in the minced garlic and dried thyme, and cook for about 30 seconds, until fragrant. Pour in the apple cider, Dijon mustard, maple syrup, and apple cider vinegar, and whisk to combine and dissolve the mustard.

9. Simmer to Reduce Let the mixture simmer for 4 to 5 minutes, whisking occasionally, until it has reduced slightly and the flavors concentrate. It should smell sweet, tangy, and savory.

10. Add the Cream Pour in the heavy cream and whisk well. Continue to simmer gently for 2 to 3 more minutes, until the sauce turns smooth, creamy, and lightly thickened enough to coat the back of a spoon. Season with salt and black pepper to taste, and adjust with a touch more vinegar or maple syrup if you want it tangier or sweeter.

11. Finish and Serve Remove the sheet pan from the oven. Drizzle the creamy apple cider Dijon sauce generously over the roasted sausage and vegetables, or serve it on the side for dipping. Garnish with fresh thyme or chopped parsley if you like, and serve warm.