Preheat the oven 400 F and line a baking sheet with parchment paper. Slice the top off of the head of garlic and add it to the baking sheet along with butternut squash and sliced shallot. Coat with avocado oil, toss with the dried herbs, and lightly season with salt and pepper. Transfer to the oven and roast for 25-30 minutes. The squash should be tender and lightly crisped on the edges. Remove from the oven and allow to cool.
While the squash roasts, prepare the pasta by bringing a pot of salted water to a boil. Boil until al dente, setting aside about ¼ cup of pasta water. Strain the pasta and set aside, lightly coating with oil to prevent sticking.
Add the ground sausage to a large pan and season with salt and pepper, crumbling the sausage until fully cooked. Once cooked, remove the pan from the heat and set it aside.
To blend the sauce, add the cooled butternut squash and shallot to a blender. Squeeze the garlic into the blender along with the pasta sauce, broth, and a splash of pasta water. Blend until fully smooth.
Pour the sauce into the pan with the ground sausage and stir until well combined.
Using a large bowl, combine the ricotta, pecorino, and about 3 oz of mozzarella. Whisk together and add the cooked pasta, along with two large ladles of the cooked sauce. Stir well.
Grease a 9x13” casserole dish and ladle some of the sauce into the bottom of the dish. Add half of the pasta, and pour more sauce on top. Layer again, with the other half of the cooked pasta, and top off with the remainder of the sauce, and the remainder of the shredded mozzarella.
Cover and transfer to a 375°F oven, baking covered for 15 minutes, before removing the cover and allowing the cheese to melt.
Remove from the oven and allow to rest for 10 minutes before serving topped with fresh thyme.