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Preheat oven to 400F/200C.
Place tomatoes in a large baking dish (I used 13x9-inch). Drizzle oil over tomatoes and toss to coat. Place the cheese in the center of the pan. Bake for 30 minutes.
Meanwhile, cook pasta per package directions; reserve about 1 cup of the pasta water. Drain and set aside and keep warm.
Melt butter and the teaspoon of oil in a large skillet over medium-high heat. Pat the shrimp as dry as you can then add to the hot pan. Cook until it turns pink and begins to brown. Set aside and keep warm.
Raise the oven temp to 450F/230C and bake for an additional 5-10 minutes or until cheese is golden brown on top and tomatoes have burst.
Remove the pan from the oven and add the basil and garlic. Stir until sauce is well mixed. At this point, you may want to add a small amount of the reserved pasta water--maybe about 2 tablespoons if the sauce seems a bit thick.
Add the cooked pasta and the shrimp. Toss so the pasta and shrimp is well coated. At this point you may wish to add some more reserved pasta water so the sauce coats everything better