Preheat oven to 400°.
Brush a jelly roll pan or shallow roasting pan with 1 tablespoon oil. Arrange tomatoes in a single layer, cut sides down, in pan. Arrange crushed garlic around tomatoes; sprinkle tomatoes with thyme and 1/4 teaspoon salt.
Bake at 400° for 30 minutes; drain juices from pan. Bake an additional 30 minutes. Remove tomatoes from pan; cool slightly. Discard juice and crushed garlic. Peel and coarsely chop tomatoes.
Heat 1 tablespoon oil in a large nonstick skillet over medium-low heat. Add chopped garlic, and cook 2 minutes, stirring frequently. Add chopped tomatoes and basil, and cook 3 minutes or until thoroughly heated. Stir in 1/2 teaspoon salt and pepper. Add pasta, and toss to coat. Sprinkle with cheese; garnish with basil sprigs, if desired.