Make the sourdough breadcrumbs: Preheat the oven to 400°F. Cut the bread into small cubes and toss with melted butter or olive oil and a pinch of salt. Spread on a baking sheet and bake for 8–12 minutes, stirring once, until dry and lightly golden. Allow to cool, then pulse briefly in a food processor to make coarse breadcrumbs. Keep them somewhat coarse for the best texture.
Roast the squash: Cut the acorn squash in half and scoop out the seeds. Brush the cut sides with olive oil or melted butter and season with salt and pepper. Place cut-side down on a baking sheet and roast at 400°F for 30–40 minutes, or until fork tender. When cool enough to handle, scoop out about 1-1.5 cups of squash flesh, leaving enough flesh inside the shells so they remain sturdy.
Brown and season the pork: While the squash roasts, heat a large skillet over medium-high heat. Add the ground pork and cook, breaking it into small pieces. Add all spices (or just use mild Italian pork and skip all spices except sage). When brown, transfer the seasoned pork to a plate, leaving the flavorful fat in the skillet.
Cook the vegetables: Add the onion, celery, and mushrooms to the skillet. Add a few tablespoons of butter if needed. Cook for 6–8 minutes, stirring occasionally, until the vegetables are tender and the mushrooms have cooked down and begun to brown.
Add the peeled & diced apple and cook for another 3 minutes, until tender but still holding its shape.
Add the garlic and cook for about 1 minute, until fragrant.
Make the filling: Return the seasoned pork to the skillet. Stir in the roasted squash and ½ cup sourdough breadcrumbs. Taste and adjust the salt and pepper as needed.
Stuff the squash: Spoon the filling generously into the roasted squash halves, gently packing it in.
Sprinkle the Gouda or sharp cheddar over the top. Finish with another small handful of sourdough breadcrumbs for a golden, crunchy topping.
Bake: Return the stuffed squash to the 400°F oven and bake for 10–15 minutes, until the cheese is melted and the filling is hot and lightly browned on top.