In a food processor, pulse the flour, sugar, and salt to combine.

Add the butter pieces and pulse until the mixture looks like coarse meal with some pea-size pieces.

Slowly add in 3 tablespoons of ice water and pulse until the dough comes together. If too dry, add the remaining water by the teaspoon and pulse until the dough just comes together.

Form the dough into a ball, put it on a sheet of plastic wrap and then press it into an 8-inch round. Wrap it tightly in the plastic wrap and refrigerate for at least 1 hour or up to 2 days before rolling out. (Note: you can also freeze the dough for up to 2 months; make sure to thaw in the refrigerator overnight before rolling it out.)

In a saucepan, heat 2 tablespoons butter over medium-low heat. Turn the heat onto medium and begin stirring to move the butter around as it starts to melt. Once melted, the butter will begin to foam and sizzle around the edges. Keep stirring to prevent butter from burning. In about 5-8 minutes from when you started, the butter will turn golden brown. The foam will slightly subside and the milk solids on the bottom of the pan will toast and become golden. It will smell intensely buttery, nutty, and rich: the desired outcome. Remove from heat once you smell the butter, nutty scent.

Add your brown sugar and vanilla extract to the browned butter. Stir until well combined and sugar has dissolved. Cool slightly as you work on the filling.

Slice your peaches thin, about ¼ inch slices. Place sliced peaches in a large bowl and add in salt, chopped fresh thyme leaves and cinnamon. Stir gently to combine. Pour in your brown butter mixture and stir to combine with the peaches so the peaches are coated in the brown butter mixture.

Preheat oven to 375 degrees fahrenheit. Place your chilled dough onto a lightly floured surface and begin rolling out to about ¼ inch thick. Place the rolled out dough onto a piece of parchment paper on a rimmed baking sheet.

Arrange the fruit mixture in the center of the chilled dough, layering the sliced peaches in a desired design, and spread out evenly, leaving a 2 to 3-inch border around the galette.

Fold edges of dough up and over fruit, pleating as needed and being careful that the folded edges of the dough do not tear (if it does, patch with dough scraps and pinch to seal).

In a small bowl, whisk your egg with a splash of water to create an egg wash. Brush the folded edges of the galette crust with the egg wash. Sprinkle a few pinches of turbinado sugar evenly over the dough.

Place galette in oven and bake, rotating halfway through, until the crust is deep golden brown everywhere, the peaches are softened, and juices are bubbling, about 45–50 minutes.

Remove from oven and cool for 5 minutes before brushing the top of the galette with the thyme simple syrup, focusing on the exposed peaches (no need to brush the crust edges).

Allow the galette to cool at least 20 minutes before serving. Serve alongside whipped cream or ice cream.