How to Make It
Melt 2 tablespoons of the butter in a large skillet over medium-high. Add oil, shallots, and garlic; cook, stirring constantly, until tender, about 1 minute. Add mushrooms and tarragon sprigs; cook, stirring occasionally, until mushrooms are browned and tender, about 13 minutes. Add brandy; cook, stirring often, until liquid is almost evaporated, about 2 minutes. Remove and discard tarragon sprigs. Stir in salt and pepper. Remove from heat; set aside.
Preheat oven to 425°F. Unroll 1 piecrust onto a lightly floured work surface. Roll into a 14-inch circle; place on a baking sheet lined with parchment paper. Sprinkle half of the cheese over piecrust, leaving a 2 1/2-inch border. Top evenly with mushroom mixture; sprinkle with remaining cheese.
Brush border of piecrust with about half of the cream. Fold edges of piecrust up and over filling toward the center, pleating as you go. (Piecrust will only partially cover filling.) Brush top of piecrust with remaining cream. Bake in preheated oven until crust and filling are golden brown, 25 to 30 minutes.
Melt remaining 1 tablespoon butter in a large nonstick skillet over medium. Add lobster; cook, tossing gently, until warmed through, 3 to 5 minutes. Arrange lobster evenly over baked galette. Sprinkle with herbs, and serve immediately.