Pasta with Roasted Tomatoes and Garlic

1            tablespoon kosher salt
8           ounces uncooked spaghetti
1/4        cup extra-virgin olive oil, divided
2           pints multicolored cherry tomatoes
4           garlic cloves, thinly sliced
1/2        teaspoon kosher salt
1/4        teaspoon freshly ground black pepper
2           ounces Parmigiano-Reggiano cheese, shaved
1/4        cup small basil leaves

1. Preheat oven to 450°.

2. Bring a large pot of water to a boil; add 1 tablespoon salt. Add pasta; cook 10 minutes or until al dente. Drain pasta in a colander over a bowl, reserving 6 tablespoons cooking liquid. Return pasta to pan. Combine reserved cooking liquid and 2 tablespoons oil in a small saucepan; bring to a boil. Boil 4 minutes or until mixture measures 1/3 cup. Add oil mixture to pan with pasta; toss to coat.

3. While pasta cooks, combine remaining 2 tablespoons oil, tomatoes, and garlic on a jelly-roll pan, tossing to combine. Bake at 450° for 11 minutes or until tomatoes are lightly browned and begin to burst. Add tomato mixture, 1/2 teaspoon salt, and pepper to pasta; toss to coat. Top with cheese and basil.