In a large pot of boiling salted water, cook the spaghetti according to package instructions until al dente. Reserve about 1 cup of pasta water, then drain and set aside.
In the same pot, melt the butter over medium heat. Add the minced garlic and sauté for about 1-2 minutes until fragrant but not browned.
Stir in the red pepper flakes and cook for another 30 seconds to infuse the butter with heat.
Reduce the heat to low and add the drained spaghetti to the pot. Toss the pasta in the garlic butter sauce until well coated. Gradually add the reserved pasta water a little at a time to achieve your desired sauce consistency.
Remove the pot from the heat and stir in the grated Parmesan cheese, chopped parsley, and lemon zest. Mix until the cheese has melted and formed a creamy sauce.
Taste the spaghetti and adjust with salt and freshly ground black pepper as needed.
Divide the spaghetti into serving bowls, sprinkling extra Parmesan and parsley over the top for garnish.
Notes
Adjust red pepper flakes to taste for desired heat.