Preparation

• Position a rack in the center of the oven and heat the oven to 400°F.
• Unfold the pastry sheet on a parchment-lined cookie sheet and score a 3/4-inch border on each side with the tip of a paring knife. Beat the egg in a medium bowl. Brush the border with some of the egg. Prick the rest of the crust all over with a fork and bake until puffed and golden, about 15 minutes. Gently press the center of the pastry to flatten large air pockets.
• Meanwhile, heat the butter in a 12-inch skillet over medium-high heat until the foam subsides. Add the mushrooms, season with 1/2 tsp. salt, and cook, stirring occasionally, until the edges start to brown, 3 to 5 minutes. Remove from the heat to cool slightly.
• Add the mushrooms, red peppers, cheese, 1 Tbs. of the tarragon, and 1/2 tsp. pepper to the remaining beaten egg and gently stir to combine. Spread the mixture over the tart, leaving the border uncovered. Sprinkle the almonds over the vegetables and continue to bake until the cheese is melted and the topping is heated through, about 10 minutes more. Remove from the oven and sprinkle with the remaining 1 tsp. tarragon. Cool slightly before serving.