Turn oven on to 400f and place rack in middle. Cut acorn squash in half and scoop out seeds with a metal spoon. Season squash with 2 Tbsp of olive oil 1/2 tsp of salt and 1/4 tsp of pepper. Turn squash cut side down on sheet pan and bake in the oven for 35-40 minutes until tender.
Remove sausage from its casing and saute in a large pan with 2 tablespoons of olive oil on medium heat for 10-15 minutes until browned and cooked through.
Add the chopped sage, 3/4 tsp of black pepper, and the 2 cups of chicken stock to the pan. Scrape off brown bits from the bottom of the pan with a wooden spoon and cook for 1 minute.
Add the 2 cups of chopped apples and 2 Tbsp of butter to the pan. Cook for 3 minutes to coat the apples and melt the butter.
Add 1/2 cup of pecorino and 3/4 cup of breadcrumbs to the pan and thoroughly mix to incorporate.
Remove the acorn squash from the oven and turn them cup side up for stuffing. Stuff the squash, mounding it higher than the edge. Place 1 Tbsp of butter on each squash half. Cover lightly with foil and return to oven 35-40 minutes more of baking. Any remaining stuffing can be placed in a baking pan and cooked alongside the squash.
Remove and test that the squash is fork-tender. If not, return to the oven for 10 more minutes. When tender, sprinkle the last 1/4 cup of pecorino onto the 4 halves and serve. Enjoy!