Meanwhile, heat olive oil in a large skillet over medium-high heat. Add shrimp and cook, stirring often, until pink all over, about 2 minutes. Add garlic and red pepper flakes; cook until shrimp is just cooked through and garlic is fragrant, about 2 minutes. Add parsley, mint, butter, and lemon zest; stir until combined.
Add spaghetti and reserved 1/2 cup pasta water to skillet; season to taste with salt and pepper. Cook, tossing constantly, until liquid thickens to form a sauce and spaghetti is hot throughout, about 1 to 2 minutes more. Transfer pasta and shrimp to 4 shallow bowls and serve immediately.
Extra idea: The flavorings in this recipe could also become a salsa verde to serve alongside grilled shrimp.