- In a saucepan, heat butter over low to medium heat until it foams and begins to brown. Stir with a spoon, scraping browned milk solids off bottom of pan. Continue cooking until butter has browned evenly and has the aroma of toasted nuts. Cool and then stir in remaining ingredients. Set aside and keep warm.
- Season fish liberally with salt and pepper, then set aside for 10 minutes. Preheat oven to 400 degrees and prepare a grill (or stovetop) for high heat. Preheat a cast-iron pan on grill until a small amount of oil begins to lightly smoke when added to the pan. Add enough oil to coat bottom of pan. Working in batches, sear grouper fillets on both sides until evenly browned, making sure to not crowd the pan. If fish isn’t cooked through after searing, transfer pan to oven and bake until barely cooked through, about 5 to 7 minutes. Fish should be opaque and easily flaked with a fork. Top with caper brown butter sauce and serve.