Bring a large pot of water to boil for the pasta.
Set a large skillet over medium-low heat and melt the butter and oil for about 1-2 minutes.
Once the butter has melted, add the garlic, red chili flakes, half of the zest and half of the lemon juice to the skillet and cook for 2-3 minutes. Remove the garlic from the sauce. Then turn off the heat.
Generously season the pot of boiling water with kosher salt. Cook the spaghetti al dente according to package instructions. Reserve 1.5 cups of pasta water. Drain the spaghetti and add it to the skillet with the lemon sauce.
Turn the heat to medium for the skillet. Add 1 cup of the pasta water along with the remaining lemon zest and juice. Season with salt and pepper. Then add the cooked spaghetti to the sauce.
Toss the pasta vigorously to emulsify the sauce. Then add the grated parmesan cheese and fresh basil. Toss everything together again in the skillet. Add more pasta water if it needs more sauce.
Plate the spaghetti and serve with additional grated parmesan cheese, lemon zest and basil. Serve immediately.