Pat fish with a paper towel before cooking—moisture inhibits browning.
Warm 3 tsp. oil in a 12-inch nonstick skillet over medium-high heat. Season fish with salt and pepper; add to skillet and cook until golden, 3 to 4 minutes. Carefully turn and cook until just cooked through, 2 to 3 minutes longer. Transfer to a platter and tent with foil to keep warm.
Add remaining 1 tsp. oil and garlic to skillet; sauté for 20 seconds. Add wine and cook, stirring to release brown bits from bottom of skillet, until liquid has reduced by about half, 1 to 2 minutes. Add broth; cook for 1 minute longer. Stir in lemon juice and capers. Remove skillet from heat; add butter and parsley and swirl until sauce is creamy. Spoon sauce over fish and serve.