Bring a pot of water to boil, add a generous pinch of salt, and cook spaghetti 1 minute less than the package directions instruct. Before draining the pasta, reserve 1 cup of water.

Heat olive oil in a medium skillet over medium heat. Add garlic and cook, stirring, until fragrant but not browned, about 1 minute. Add red pepper flakes and stir for a few more seconds.

Add lemon juice and white wine, increase heat to medium-high, and simmer until liquid is reduced by half, about 5 minutes. Season with salt and pepper.

Add butter and 2 tablespoons of pasta water, and turn off heat once the butter's melted.

Add the pasta to the pan, followed by the lemon zest and Parmesan cheese, tossing to coat. Add more pasta water as needed, 1 tablespoon at a time. Taste and add more salt and pepper, as needed.

Serve topped with Parmesan cheese, thyme, and red pepper flakes.