Preheat an oven to 425 degrees. Line a baking sheet with parchment paper. Rub about 1 tablespoon of oil on the insides of the delicata squash. Sprinkle with salt and pepper and place cut side down on the baking sheet. Place in the oven and bake until the flesh is soft, about 30-45 minutes.
Heat a large saute pan to medium heat and add the sausage, stirring. After a few minutes, add the mushrooms and onion. Continue to cook and stir until the sausage is browned and cooked through, and the mushrooms and onions are soft.
* If using beans or tofu, add them after the mushrooms and onions have softened. You can also add some spices like salt, pepper, paprika, coriander, and/or cumin.
Remove the squash from the oven and stuff the cavities with the sautéed mixture. Top with cheese and bake in the oven for about 5 minutes.
Add all of the sauce ingredients to a food processor or blender and mix until smooth.
Serve the stuffed squash with the green sauce on top.