Step 1: Begin by preheating your oven to 425°F. Cut the butternut squash into half-inch cubes. In a large mixing bowl, combine the squash, red onion, and two tablespoons of olive oil, tossing until well coated. Spread the mixture evenly across two large baking sheets, and season with salt and pepper. Roast in the oven until the vegetables are fork-tender and golden, approximately 30 minutes, remembering to toss halfway through cooking.

Step 2: In a large pot filled with boiling salted water, cook the bucatini according to the package instructions. Once cooked, reserve ½ cup of the pasta water and then drain the remaining liquid.

Step 3: Heat the remaining tablespoon of olive oil in a large skillet over medium heat. Add the sausage, breaking it up with a wooden spoon as it cooks until it turns golden and crispy, which should take about 10 minutes. Once cooked, transfer the sausage to a plate to keep warm.

Step 4: Return the skillet to the heat and add the butter. Allow the butter to cook until it becomes foamy, then reduce the heat to medium-low. Continue stirring until the butter emits a nutty aroma and takes on a deep golden hue, which should take around 4 minutes. Add the minced garlic, sage, and thyme, cooking for an additional minute until fragrant before removing the pan from the heat.

Step 5: To the skillet, add the cooked bucatini, sausage, roasted squash, and ¼ cup of the reserved pasta water. Toss everything together to combine. If necessary, add more pasta water to help the sauce come together smoothly.

Step 6: Finally, top the pasta with shaved Parmesan before serving.