Bring a large pot of salted water to a boil. Cook pasta until al dente, reserving 1 cup of pasta water before draining.
While pasta cooks, zest the lemon and set aside. Juice the lemon into a cup and set aside.
In a large skillet over medium-low heat, melt 1 tbsp butter. Add garlic and sauté until fragrant, about 30–60 seconds.
Pour in heavy cream and most of the lemon zest. Allow the cream to warm until it begins to gently bubble around the edges.
Add remaining butter 1 tablespoon at a time, whisking continuously to fully incorporate before adding the next piece.
Stir in parmesan cheese and whisk until melted and smooth. Season with black pepper and a small pinch of salt.
Remove the pan from heat. Add lemon juice and ½ cup reserved pasta water. Whisk until the sauce is smooth and slightly loosened.
Return skillet to medium-low heat. Add drained pasta and toss to coat.
Let the pasta cook for 1–2 minutes, tossing frequently, until the sauce thickens and clings to the pasta.
Taste and adjust seasoning if needed.
Serve immediately topped with fresh basil, extra parmesan, and reserved lemon zest.