Step 1

Bring a large pot of salted water to a boil. Add the pasta and cook until 1 minute shy of al dente (check the package directions for timing). Drain the pasta, reserving 1/2 cup pasta cooking water.

Step 2

Place the pot over medium-high heat and add 4 tablespoons of the oil. Add the garlic and cook until golden, about 2 minutes. Stir in about half the tomatoes, the olives, thyme, 1/2 teaspoon salt, black pepper, and red pepper flakes. Cook until the tomatoes just begin to soften, 3 to 5 minutes.

Step 3

Reduce the heat to low and stir in the goat cheese and cream, letting it melt into a sauce. Remove from the heat and stir in the drained pasta, the remaining tomatoes, Parmesan, and remaining 2 tablespoons oil and toss until evenly coated. If the mixture looks dry, add a little pasta cooking water, a tablespoon at a time. Taste a piece of pasta to make sure it's cooked through (if not, put the pot back on the heat for another minute or so, stirring). Stir in the basil.

Step 4

To serve, top the pasta with more parmesan, red pepper flakes, and oil.