Bring a large pot of salted water to a boil and cook spaghetti according to package directions until al dente.
While pasta cooks, heat butter and olive oil in a nonstick skillet over medium heat.
Add garlic and sauté for 1–2 minutes until fragrant.
Add cherry tomatoes, red pepper flakes, kosher salt, and black pepper. Cook for 6–8 minutes, stirring occasionally, until most tomatoes burst.
Use tongs to transfer cooked pasta directly into the skillet. Reserve about 1/2 cup pasta water.
Stir in reserved pasta water to loosen the sauce. Add parmesan cheese and sliced basil, tossing until well combined.
Serve immediately with extra basil and parmesan if desired.