Step 1Heat the oven to 400 degrees. Cut 2 (15-inch-square) pieces of parchment paper or aluminum foil and lightly oil one side.
Step 2Heat 1 tablespoon of oil in a large nonstick skillet over high heat. When the oil shimmers, add the mushrooms, three-fourths teaspoon salt and cook, tossing frequently, until the mushrooms start to soften, 2 to 3 minutes. They'll begin to sizzle and shine as they release their moisture.
Step 3Add the shallots, tarragon and white wine, reduce the heat to medium and cook until the wine evaporates, about 2 minutes. The mushrooms should be tender and lightly browned in places. Season with just a dash of black pepper.
Step 4Lightly season each halibut steak with three-eighths teaspoon salt and a few grinds of pepper. Place a steak in the center of each piece of parchment paper and spoon the mushrooms evenly over the steaks. Crinkle together the edges of the parchment paper to make an airtight packet, with some room left for the packet to expand. Place the packets on a baking sheet. (The recipe can be made to this point several hours in advance and refrigerated until ready to cook.)
Step 5Bake the packets until they puff slightly, 25 to 30 minutes (you may need to unwrap the packets a little to make sure the halibut is firm and opaque). Remove from the oven and place the packets, still sealed, on a platter. To serve, open the packets and divide the halibut and mushrooms onto plates.