Arrange tomatoes in one even layer on a sheet pan. Toss with 2 tablespoons of olive oil and spinkle with sea salt. Roast tomatoes for 15-20 minutes until skins burst. Remove from heat.
In the meantime, bring a large pot of salted water to a boil. Cook pasta according to package instruction. When draining, reserve 1 cup of the starchy pasta-cooking water.
While pasta cooks, heat remaining 2 tablespoons of olive oil on medium-high setting in a large saucepan. Add garlic and cook for about 1-2 minutes until garlic becomes fragrant and starts to brown. Discard garlic. Add hot pasta and tomatoes to the pan. Stir in pasta-cooking water a little at a time until desired consistency. Cook together for about 2 minutes to marry flavors.
Serve sprinkled with fresh basil and shaved Parmigiano.