Rinse and drain asparagus. Snap off and discard tough stem ends.
Rinse fish and pat dry. In a plastic bag, combine flour, salt, and pepper. Shake 1 or 2 pieces of fish at a time in flour mixture to coat, shaking off excess as you lift fish from bag. Discard leftover flour mixture.
Put 1 tablespoon butter in a 10- by 15-inch baking pan and 2 tablespoons butter in another 10- by 15-inch pan. Set pans in a 500° oven until butter is melted, 1 to 2 minutes. Place asparagus in pan with smaller amount of butter; turn to coat spears. Place fish in remaining pan; turn to coat in butter and lay in a single layer. Return pans to oven and roast until asparagus is tender-crisp to bite and fish is opaque but still moist-looking in center of thickest part (cut to test), 4 to 5 minutes.
Transfer asparagus and fish to a platter and keep warm.
Pour wine into fish-roasting pan and add 3 tablespoons tarragon. Set pan over two burners on high heat and bring to a boil. Stir until wine is reduced to 1/3 cup, about 2 minutes. Remove from heat and stir in remaining 1 tablespoon butter until blended. Pour sauce into a bowl.
Scatter remaining 1/2 tablespoon tarragon over fish. Serve fish and asparagus with sauce to add to taste.
Wine pairing: A classic Sauvignon Blanc, with hints of lemon and grass, is a natural match for the asparagus, wine sauce, and delicate sole. The minerals and lemon in Pinot Gris also make a fine pairing.
Note: Nutritional analysis is per serving.