For the Crust:

1. MIX DRY INGREDIENTS: Whisk the flour and salt together in a medium mixing bowl.
2. ADD COLD BUTTER: Add the cubed butter and toss in the dry flour mixture, separating any pieces that stick together until lightly coated. Using the pastry cutter (you can also use two forks), mix in the cold butter cubes until the mixture resembles a coarse meal and the butter is pea-sized.
3. MIX REMAINING WET INGREDIENTS: In a separate small bowl, mix together the sour cream, lemon juice, and ice water (not any ice cubes). Add the liquid mixture to the flour and mix until the dough is combined.
4. ROLL OUT DOUGH: Move the dough to a lightly floured surface and knead a few times until it comes together and you can shape it into a thick disk. Wrap the dough in plastic wrap and refrigerate for at least an hour and up to 3 days.

For the Mushroom Filling:

1. HEAT PAN: Heat a large sauté pan over high heat. Add the oil and wait 1 minute. Then add 1 tablespoon of butter, and when it starts to foam, add the mushrooms, spreading them evenly in the pan. Season with salt and pepper.
2. COOK MUSHROOMS: Sauté the mushrooms, stirring occasionally, until they’ve released their moisture, have become tender, and have begun to caramelize (get crispy edges), about 5 minutes.
3. ADD ONIONS & THYME: Next, reduce the heat to medium and add the onions and thyme. Cook, stirring frequently, until the onions have softened, about 5 minutes.
4. ADD GARLIC: Add the garlic and cook until fragrant, about 1 minute.
5. LET COOL: Remove the mushroom and onion mixture from the heat and cool to room temperature.

For the Salad:

1. SEASON HERBS: Toss the herbs in a small bowl with salt and pepper. Drizzle with the olive oil (about 1 tablespoon) and a squeeze of lemon juice (about 1-2 teaspoons) and toss together.

To Assemble:

1. PREP: Preheat the oven to 400 degrees. Line a baking sheet with parchment paper.
2. ROLL OUT DOUGH: On a lightly floured surface, roll out your dough into a 12-inch circle or shape of your choice. Transfer your dough to the prepared baking sheet.
3. MAKE MUSHROOM MIXTURE: In a bowl, gently stir together the cooled mushroom mixture and the grated cheese. Spoon the mixture in an even layer in the center of the dough, leaving a 2-3 inch border. 
4. PREP THE GALETTE BORDER: Turn the border back over the mushroom mixture (towards the center of the galette). Prepare your egg wash by whisking together the egg and milk. Brush the crust with the prepared egg wash.
5. BAKE: Bake until the crust is golden brown, about 35-40 minutes. Make sure to rotate the pan halfway through to ensure even baking.
6. COOL: Let cool for at least 10 minutes and top with herb salad (you can also serve the salad on the side).