How to Make It
Bring a large pot of moderately salted water to a boil. Cook the pasta until al dente. Drain, reserving 1/2 cup of the cooking water.
In a large skillet on medium-high heat, heat the olive oil. Add the sliced garlic and cook until the pieces begin to cook through and shrivel around the edges, about 1 minute. Just before the garlic pieces start to brown, quickly add the tomatoes to the pan and generously season with salt. The oil will start to slightly fry the tomatoes, continue to cook tomatoes on high heat for about 3 minutes. Lower the heat to low and add the black olives and crushed red pepper flakes, and simmer for about 4 minutes.
Add the cooked pasta to the pan, along with the reserved pasta water. Toss the pasta in the pan or stir until evenly coated with the sauce. Stir in the Parmigiano-Reggiano, lemon zest and chopped basil. Season with salt and serve.