Bring a large pot of salted water to a boil. Cook 1 pound of pasta per package instructions.
In a large saucepan over medium heat, melt together 5 tablespoons butter and 3 tablespoons extra-virgin olive oil. Using a microplane or the smallest hole on a box grater, grate the zest of 1 lemon and 2 garlic cloves into the sauce pan. Stir to cook the lemon and garlic for several minutes, then turn the heat to low.
Once the pasta is cooked, reserve 1 cup of the pasta cooking water, then drain the pasta.
To the saucepan with the lemon butter, add the drained pasta, 1/3 cup grated Parmesan cheese, the juice from the zested lemon, 1/3 cup of the reserved pasta cooking water, and a pinch of salt.
Toss everything together until the Parmesan melts into a creamy sauce. Add another splash of the reserved pasta water if you need things a bit saucier.
Serve immediately and garnish with a sprinkle of parmesan and several grinds of fresh pepper.