Bring a large pot of salted water to a rolling boil over high heat. Add the spaghetti, cooking it according to package instructions until al dente, about 8-10 minutes. Reserve around 1 cup of the starchy pasta water a few minutes before draining.

While the pasta cooks, heat a large skillet over medium heat. Add unsalted butter and let it melt until foamy. Stir in the lemon zest and minced garlic, cooking for 1-2 minutes until fragrant, being careful not to burn the garlic.

Once the spaghetti is cooked, use tongs to transfer it directly from the pot into the skillet. Pour in about ½ cup of the reserved pasta water and toss everything together until the pasta is lightly coated.

Reduce the heat to low and add half of the grated Parmesan cheese to the skillet, tossing to combine smoothly. Squeeze fresh lemon juice over the pasta and add the remaining cheese. Keep tossing until the sauce is creamy and glossy, adding more pasta water if necessary.

Taste and adjust the seasoning with sea salt and black pepper. Garnish with additional lemon zest and chopped fresh parsley or basil before serving.