Boil the pasta: Bring a large pot of well-salted water to a rolling boil. Cook the pasta to al dente according to package directions.
Scoop out at least 1 cup pasta water before draining.
Start the sauce base: In a large skillet over medium heat, warm the butter and olive oil. Add the garlic and sauté for 30–45 seconds until fragrant, not browned.
Add cream: Pour in the cream and bring to a gentle simmer. Stir often and let it reduce slightly for 2–3 minutes so it thickens a bit.
Stir in pesto: Lower the heat and whisk in the basil pesto until the sauce turns evenly green and smooth.
If it seems too thick, loosen with a splash of pasta water.
Cheese and lemon: Add Parmesan, lemon zest, and 1 teaspoon lemon juice. Stir until the cheese melts and the sauce becomes glossy. Taste and adjust with salt and pepper.
Toss with pasta: Add the drained pasta to the skillet.
Toss vigorously, adding pasta water a little at a time until the sauce clings to the noodles and looks silky.
Optional add-ins: Fold in spinach (it will wilt quickly), peas, or cooked chicken. Warm through for 1–2 minutes. Avoid boiling the sauce once the pesto is in.
Serve: Plate immediately with extra Parmesan, a twist of black pepper, and a squeeze of lemon if you like.
A few torn basil leaves on top are a nice touch.