Heat the olive oil in a large skillet over medium heat until shimmering.
Add the sliced garlic and red pepper flakes and sauté, stirring frequently, until the garlic is golden and fragrant, about 2 minutes; do not let it burn.
Add the shrimp to the skillet in a single layer, sprinkle with kosher salt and paprika, and cook, turning once, until the shrimp are pink and opaque, about 2–3 minutes total depending on size.
Remove the skillet from the heat, stir in the chopped parsley, toss to combine, and serve immediately.