Bring a large pot of salted water to a boil and cook pasta according to package directions until al dente. Just before draining, reserve 1 cup of the pasta cooking water. Drain.
Melt 4 tablespoons butter in a large skillet over medium heat. Add the garlic and pepper and cook 1-2 minutes, until the butter is browning, and the garlic is golden and fragrant. Reduce the heat to low and add 1/2 cup pasta water, the pasta, remaining butter, and pecorino. Tossing until melted. Remove from the heat, add 3/4 cup basil and toss, adding in more pasta water if needed to thin the sauce.
In a bowl, combine the tomatoes, remaining 1/4 cup basil, olive oil, red pepper flakes, and a pinch of salt.
To serve, divide the pasta among bowls and serve topped with tomatoes.
