Heat olive oil in a heavy skillet over high heat until it just begins to smoke. Place shrimp in an even layer on the bottom of the pan and cook for 1 minute without stirring.

Season shrimp with salt; cook and stir until shrimp begin to turn pink, about 1 minute.

Add garlic and red pepper flakes; cook and stir for 1 minute.

Stir in lemon juice, caper brine, 1 piece of butter, and 1/2 of the parsley; cook until butter has melted, about 1 minute.

Reduce heat to low and stir in remaining 3 pieces butter. Cook and stir until butter has melted, sauce is thick, and shrimp are pink and opaque, 2 to 3 minutes.

Remove shrimp with a slotted spoon and transfer to a bowl; continue to cook butter sauce, adding water, 1 teaspoon at a time, if too thick, about 2 minutes. Season with salt to taste; serve shrimp topped with the pan sauce and remaining parsley.