Bring a large pot of salted water to a boil. Cook fettuccine until just al dente, about 1 minute less than package directions. Reserve 1 cup pasta water, then drain.

Melt butter in a skillet over medium heat. Add garlic and cook 30 seconds until fragrant.

Pour in cream and simmer 2 to 3 minutes until slightly thickened. Reduce heat to low, whisk in Parmesan a handful at a time, then remove from heat and stir in pesto. Season with salt and pepper.

Add drained pasta and a splash of reserved pasta water to the skillet. Toss well, adding more pasta water as needed until the sauce is glossy and coats the pasta.

Serve immediately with extra Parmesan, black pepper, and fresh basil.