Preheat the oven to 375℉.
In a large, oven-safe skillet, heat the oil over medium heat. Add the shallot, garlic, 2 tablespoons of minced sage, and red pepper flakes and cook, stirring, until tender, taking care not to burn.
Pour in the wine and cook, stirring, until reduced by half, about 3 minutes.
Add the heavy cream, pumpkin, broth, salt, pepper, cayenne, allspice, and nutmeg and whisk until well combined. Bring to a simmer.
Once it comes to a simmer, remove from heat and add the tortellini. Gently toss so that it is well combined and spread into an even layer across the skillet. Top with the parmesan, mozzarella, and remaining sage.
Transfer to the oven and bake until the tortellini is tender and the cheese and golden, 10 to 12 minutes.