Bring a large pot of salted water to a boil. Add spaghetti and cook according to package instructions until al dente. Reserve 1/3 cup pasta water, drain, and set pasta aside.

While the pasta cooks, heat olive oil in a large skillet over medium heat. Add garlic (and chili, if using) and sauté for 1-2 minutes until fragrant, but not browned.

Pat shrimp dry with a paper towel. Add shrimp to the skillet in a single layer. Season with salt and pepper. Cook for about 2 minutes on one side, then flip and cook another 1-2 minutes until opaque and just cooked through. Remove shrimp to a plate.

Add lemon zest and juice to the skillet. Stir to deglaze, then add the drained pasta, tossing well to coat. If needed, add reserved pasta water a little at a time to loosen the sauce.

Return the shrimp (with any juices) to the pan. Toss in chopped parsley. Mix everything gently until heated through.

Taste and adjust seasoning. Serve immediately, topped with parmesan and lemon wedges if desired.