Step 1
Whisk together the flour and 1/4 teaspoon each salt and pepper in a shallow plate, and coat the fish on one side only. Shake off excess flour and transfer fish flour-side up to a sheet pan or cutting board. Reserve 1-1/2 teaspoons of the flour mixture for the sauce.
Step 2
Heat 1 tablespoon of the oil in a large stainless steel or well-seasoned cast iron skillet over high heat until just smoking. Add as much sole as will fit comfortably in a single layer, flour-side down and cook until bottom is browned, about 2 minutes. With two spatulas, turn the fish and remove pan from the heat. Let stand until just cooked through, about 30 seconds to 1 minute longer. Remove fish to a platter, cover to keep warm and wipe out the skillet. Repeat with the remaining oil and fish. Wipe out the skillet to make the sauce.
Step 3
Heat the olive oil, fennel, fennel seed and red pepper flakes in the same skillet over medium high heat, seasoning with salt and pepper and stirring frequently, until the fennel is softened, about 3-4 minutes.
Step 4
Whisk in the reserved flour and cook 30 seconds. Whisk in the wine, water and lime juice and cook 3-4 minutes or until lightly thickened. Whisk in the butter and season with salt and pepper. Spoon over the fish and garnish with reserved fennel fronds.
