Cut acorn squash in half vertically and scoop out seeds. Brush interiors with 1 tablespoon olive oil and sprinkle with salt and pepper.
Place cut-side down on a sheet pan and bake 25-40 minutes, or until squash is soft.
While squash is baking, heat remaining olive oil in a large skillet over medium heat. Add sausage and brown, breaking it apart into small pieces.
Add onion and apple and cook until soft, about 8 minutes.
Add garlic and thyme and cook another 3 minutes.
When squash is done baking and cooled slightly, scoop out flesh, leaving about 1/4-inch flesh inside the skin. Do not discard skin. Mix squash flesh with meat mixture.
Mound filling back into squash halves and return to oven for 15 minutes.
When done, top each squash half with a fried egg and add salt and pepper to taste.