Instructions

1. Place 1 cup whole-wheat flour, 3/4 cup all-purpose flour, and 1 teaspoon kosher salt in a large bowl and whisk to combine. Add 1/3 cup of the olive oil and mix with a fork until crumbly. Add 1/3 cup water and 1 teaspoon of the red wine vinegar and continue to mix until a soft dough ball forms. Wrap the dough tightly in plastic wrap and refrigerate while you prepare the filling, at least 45 minutes.
2. Halve and thinly slice 1 medium red onion. Tear 1 pound fresh mushrooms into bite-sized pieces. Strip the leaves from 1 small bunch rosemary sprigs and coarsely chop to get 1 tablespoon.
3. Heat 1 tablespoon of the olive oil in a large skillet over medium heat until shimmering. Add the onion and sauté until softened and golden, 5 to 7 minutes. Transfer to a medium bowl.
4. Add 1 tablespoon of the olive oil to the pan and add half the mushrooms in a single layer. Cook undisturbed until browned on the bottom, about 5 minutes. Season with 1/4 teaspoon of the kosher salt and 1/8 teaspoon of the black pepper and cook, stirring once or twice, until the mushrooms are browned all over and tender, 2 to 3 minutes more. Transfer to the bowl with the onion.
5. Add the remaining 1 tablespoon olive oil to the pan and repeat cooking the remaining mushrooms with the remaining 1/4 teaspoon kosher salt and 1/8 teaspoon black pepper. About a minute before the mushrooms are ready, add about three quarters of the rosemary (reserve the remaining for garnish) and sauté until fragrant, about 1 minute.
6. Remove from the heat. Add the remaining 1 teaspoon red wine vinegar and stir to combine. Transfer to the bowl of mushrooms and onion and stir to combine. Let cool while the dough finishes chilling.
7. Arrange a rack in the middle of the oven and heat the oven to 400°F. Tear a piece of parchment paper, roughly the size of a large rimmed baking sheet, and place it on a work surface. Lightly dust the parchment paper with flour.
8. Unwrap the dough and place it on the parchment. Sprinkle the dough with flour and roll into a round about 12-inches wide. Transfer the parchment paper with the rolled-out dough on it to a rimmed baking sheet.
9. Spread 1 tablespoon Dijon mustard evenly onto the dough with the back of a spoon or a butter knife, leaving a 1 1/2- to 2-inch border. Spoon the mushroom mixture evenly over the mustard. Tear 4 ounces Brie cheese with its rind into bite-sized pieces and scatter on top of the filling. Gently fold the edges of the dough over the filling, pleating it about every 2 inches.
10. Bake until the crust is firm and golden-brown, and the cheese is melted and browned in spots, about 30 minutes. Let the galette cool for at least 5 to 10 minutes before serving. Garnish with the reserved rosemary and serve warm, cut into wedges.