Position racks in the upper and lower thirds of the oven and heat the oven to 450°F. Put a large rimmed baking sheet on each rack.
Heat 2 Tbs. of the butter with the oil in a 12-inch skillet over medium-high heat until the foam from the butter subsides. Add the artichokes cut side down and cook without stirring until light golden, 2 to 3 minutes. Add the garlic and cook, stirring, just until fragrant, about 30 seconds. Stir in 2 Tbs. of the vermouth and remove from the heat. Stir in the tomatoes, mint, and 1/2 tsp. each salt and pepper. Transfer to a plate and set aside to cool.
Cut four 12x18-inch sheets of heavy-duty foil. Set one piece of fish on one side of each sheet and season each with 1/8 tsp. each salt and pepper. Spoon the artichoke-tomato mixture over the fish, dividing it equally. Top each with 1 tsp. of the remaining vermouth and dot with 1 tsp. of the butter. Fold the foil over the fish and crimp the edges to seal completely, leaving some air space inside.
Transfer the packets to the hot baking sheets and bake until the packages puff, about 15 minutes. To test for doneness, plunge a paring knife through the foil and the fish and hold it there for 5 seconds. Touch the side of the knife to your lip; if it feels warm the fish is cooked through. Transfer the packets to plates and serve.
nutrition information (per serving):
18, Fat Calories
160, Saturated Fat
33, Monounsaturated Fat
8, Polyunsaturated Fat
Photo: Scott Phillips