Preheat oven to 425°.
Place squash and bell pepper in a large bowl. Add 1 tablespoon oil; toss well. Arrange vegetables in a single layer on a jelly-roll pan coated with cooking spray. Sprinkle with 1/2 teaspoon salt, rosemary, and black pepper. Bake at 425° for 40 minutes, stirring once.
Place goat cheese in freezer 10 minutes. Cut cheese crosswise into 8 equal rounds. Place breadcrumbs in a shallow bowl. Dredge each round in breadcrumbs; place on a baking sheet. Bake at 425° for 6 minutes.
Cook pasta according to package directions, omitting salt and fat. Drain, reserving 1/2 cup pasta cooking water. Return pasta to pan; add reserved pasta cooking water, remaining 1 1/2 teaspoons oil, remaining 1/2 teaspoon salt, red pepper, and garlic, tossing to coat. Place 1 1/4 cups pasta in each of 8 shallow bowls; top each serving with about 1/2 cup squash mixture and 1 goat cheese round. Garnish with rosemary sprigs, if desired.