In a large bowl, whisk together 2.5 cups flour and 1 tsp salt. Add 0.75 cup cold cubed butter. Using a pastry cutter or your fingertips, cut the butter into the flour until pea-sized crumbs remain (some pea-sized pieces okay).

Add ice water

Drizzle 6 tablespoons ice water over the mixture, mixing with a fork until the dough just comes together. Add an extra tablespoon if very dry; do not overwork. The dough should hold when pressed but still be slightly shaggy.

Chill

Turn dough onto lightly floured surface, gather into a disk about 1 inch thick, wrap in plastic, and chill at least 30 minutes (up to 2 hours).

Filling

Prepare vegetables

While dough chills, heat 1 tablespoon butter and 1 tablespoon olive oil in a large skillet over medium heat.

Cook onions

Add the thinly sliced medium onion and a pinch (about 1/4 tsp) of the salt to the skillet. Cook, stirring occasionally, until translucent and beginning to caramelize, about 8–10 minutes. Reduce heat if browning too quickly.

Cook mushrooms

Increase heat to medium-high, add the sliced mushrooms and remaining 2.5 tsp salt (see ingredient salt total). Cook without crowding so they brown, stirring occasionally, until most moisture evaporates and mushrooms are golden, about 6–8 minutes.

Add garlic and thyme

Add the minced garlic and 1 tsp fresh thyme leaves (or 1/2 tsp dried). Cook 30–45 seconds until fragrant.

Thicken filling

Sprinkle 1 tablespoon flour over the vegetables and stir for 1 minute to remove raw flour taste. Slowly pour in 1/2 cup milk while stirring to avoid lumps; simmer 1–2 minutes until filling thickens slightly.

Finish filling

Remove skillet from heat. Stir in 1 cup grated Gruyère and 2 oz softened cream cheese until melted and smooth. Season with 1/2 tsp black pepper and 1/2 tsp lemon juice if using. Taste and adjust seasoning. Transfer filling to a bowl and cool to room temperature (or refrigerate briefly) before assembling so it won't melt the dough or melt too much cheese during shaping.

Assembly/Finish

Preheat oven and prepare pan

Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper or lightly grease an oven-safe tart pan or baking sheet.

Roll out dough

On a lightly floured surface, roll chilled dough to about 1/8–1/4 inch thick into a roughly 12-inch circle for a single large galette or divide into 4 equal pieces and roll into 4 smaller rounds (~7–8 inch) for individual pastries. Transfer to prepared baking sheet, using parchment to help lift if needed.

Fill

Leave a 1.5–2 inch border around the edge. Spoon the cooled mushroom-onion-cheese filling into the center, spreading evenly but leaving the border free.

Fold edges

Fold the exposed border over the filling in pleats to create a rustic edge, overlapping slightly as you go. For individual pastries, fold edges up to form small rounds or crimp as desired.

Egg wash and finish

Beat the whole egg with 1 teaspoon water and brush lightly over the exposed dough edge. Sprinkle with a pinch of coarse sea salt if desired.

Bake

Bake in the preheated oven for 20–25 minutes for a large galette (or 15–18 minutes for smaller individual pastries), until the crust is golden and the filling is bubbling at the center.

Rest and serve

Remove from oven and let rest 5–10 minutes to set. Slice and serve warm or at room temperature. Leftovers keep refrigerated up to 3 days; reheat at 350°F (175°C) for 8–10 minutes to crisp the crust.