Bring a large pot of water to a boil and salt it generously until it tastes like seawater. This properly seasons your pasta from the inside out.
Cook pasta according to package directions until just al dente, typically 8-10 minutes. Before draining, reserve 1 cup of the starchy pasta water.
While pasta cooks, melt butter in a large skillet over medium heat until it begins to foam. Add minced garlic and cook for 30-60 seconds until fragrant but not browned. Garlic burns quickly, so watch carefully.
Reduce heat to medium-low and add lemon zest, lemon juice, and red pepper flakes if using. Stir to combine and let the mixture simmer gently for about 1 minute to meld flavors.
Add the drained pasta directly to the skillet along with ¼ cup of reserved pasta water, tossing vigorously with tongs to coat every strand. The starchy water helps create a silky emulsion.
Gradually sprinkle in the Parmesan cheese while continuing to toss the pasta. The residual heat will melt the cheese into a smooth sauce. Add more pasta water a tablespoon at a time if it seems dry.
Drizzle in the olive oil and add the fresh parsley, tossing once more to incorporate. Taste and adjust seasoning with salt and pepper.
Serve immediately in warmed bowls, topped with additional Parmesan cheese, fresh cracked pepper, and a small sprinkle of lemon zest if desired.