In a medium bowl (large enough to hold shrimp), whisk together cornstarch, salt and pepper. Add shrimp and gently toss with fingers to coat evenly.
Heat olive oil and 2 tablespoons of butter in a large skillet over medium-high heat until hot and foamy. Add shrimp in a single layer and cook without stirring until one side is crisp, about 2 minutes. With a thin spatula, flip each shrimp to crisp on the second side, about 2 minutes more. Transfer shrimp to clean plate.
Add broth, lemon juice, and capers to skillet. Bring to boil, scraping up any browned bits. Add remaining tablespoon of butter and stir to melt. Return shrimp to skillet and stir gently until shrimp is coated with sauce and heated through, about 1 minute. Remove from heat and transfer to platter if desired. Top with parsley and lemon slices if using and serve.