Cut your monkfish into 1/2 inch medallions. Remove any gray membrane from the fish. Place flour in a baggie large enough for the fish.
Melt the butter in a small skillet. Add the shallots and garlic and cook on medium until both the butter and shallots have lightly browned and acquired a nutty aroma. Stir in capers, tarragon, lemon juice, and chicken broth until just warmed and remove from stove. Set aside.
Place fish into baggie and shake around till fish is covered. Heat olive oil over medium heat. Add coated monkfish medallions and cook approximately 5-6 minutes on each side until golden brown.
Briefly warm the sauce. Divide the monkfish between two plates and drizzle with sauce.