Preheat the oven to 375 degrees F (190 degrees C).
Cut butternut squash in half, lengthwise. Scoop out and throw away seeds. Brush the cut side of squash with 1 teaspoon oil. Place cut-side down onto a baking sheet and cover with aluminum foil.
Bake in the preheated oven until tender, about 30 minutes. Remove and let cool, 5 to 10 minutes. Leave the oven on.
Heat 1 tablespoon oil in a large sauté pan or skillet over medium-high heat. Cook and stir ground beef in hot oil until browned and crumbly, about 10 minutes. Add onion, apple, and garlic. Continue to cook, while stirring around, until fruit and vegetables are slightly soft, 5 to 10 minutes more.
Turn squash over and place cut-side up onto the baking pan. Fill the centers of squash with beef mixture. Dot each with 1 tablespoon butter and sprinkle with 1 tablespoon brown sugar.
Bake, uncovered, in the preheated oven until brown sugar is golden brown, 15 to 25 minutes. Take squash out of the oven and sprinkle each half with goat cheese. Serve.