Bring a large pot of salted water to boil and cook pasta according to package directions until al dente, reserving 1 cup of pasta water before draining.
While pasta cooks, heat olive oil in a large skillet over medium heat and add sliced garlic, cooking until fragrant and just golden, about 2-3 minutes.
Add cherry tomatoes and red pepper flakes to the skillet, cooking until tomatoes just begin to soften, about 3-4 minutes.
Add drained pasta to the skillet along with 1/2 cup pasta water, tossing to combine and adding more pasta water as needed to create a silky sauce.
Remove from heat and stir in Parmesan cheese, torn basil, salt, and pepper, tossing until cheese melts and coats the pasta.
Serve immediately with extra Parmesan and fresh basil on the side.