Preheat the oven to 400 degrees F (200 degrees C).
Brush the inside of the spaghetti squash with 1 tablespoon olive oil and place cut-side down on a baking sheet.
Bake in the preheated oven on the middle rack until squash is easily pierced with a fork, about 25 minutes.
Meanwhile, heat 1 tablespoon olive oil in a skillet over medium-low heat and cook garlic until fragrant, about 1 minute. Add bell pepper. Cook and stir until softened, about 3 minutes. Stir in tomatoes and basil, cover, and cook, stirring occasionally, until soft, about 10 minutes.
Remove spaghetti squash from oven, cool slightly, and shred the cooked squash into spaghetti-like strands. Place strands in a bowl. Add bell pepper mixture, goat cheese, salt, and black pepper and mix until well combined. Spoon mixture back into the squash halves. Sprinkle with breadcrumbs and butter cubes.
Bake in the preheated oven until filling is bubbly and bread crumbs are browned, about 15 minutes.