Heat garlic in oil in a saucepan over low heat until pale gold, about 10 minutes. Strain; reserve oil and garlic. Let cool.
Combine tomatoes, 1/4 cup basil, the capers, lemon zest, red-pepper flakes, and 1/2 teaspoon salt in a large bowl. Pour garlic oil and chips over tomato mixture. Marinate, covered, tossing occasionally, for 30 minutes.
Add warm pasta to bowl, and toss gently. Top with remaining 1/2 cup basil. Season with pepper. Sprinkle with lemon zest.
Follow these steps when you cook the pasta for this dish: Bring a large pot of water (6 quarts) to a boil -- you want enough water so the pasta can move around. Season the water with 1/4 cup coarse salt. (The water should be well seasoned; think "salty like the sea.") Cook 1 pound of pasta until al dente. Drain, reserving at least 2 cups cooking water. The pasta releases starch as it cooks, and the starchy water is essential to the sauce.
5 garlic cloves, thinly sliced
1/2 cup extra-virgin olive oil
2 pounds heirloom tomatoes, sliced into 1/2-inch wedges
3/4 cup torn fresh basil
3 tablespoons salt-packed capers, preferably Sicilian, rinsed and chopped if large
2 teaspoons finely grated lemon zest, plus more for sprinkling
1/4 teaspoon crushed red-pepper flakes
Coarse salt and freshly ground pepper
1 pound croxetti or other flat pasta, such as maltagliati or pappardelle, cooked until al dente