Bring a large pot of salted water to a boil and cook pasta to one minute less than the package directions state.
Meanwhile, heat butter and oil in a large skillet until the butter starts to foam. Add the garlic and cook for 1 minute. Add the thyme, the lemon zest, and the lemon juice. Season with salt and pepper to taste.
Reserve one cup of pasta water and drain the pasta. Add the pasta to the pan with the sauce along with ½ cup of the reserved pasta water and toss to coat, adding more pasta water as needed.
Serve with grated Parmigiano Reggiano, more lemon zest and pepper.