To make the crust, combine flour, zest, sugar, salt, and cold butter in a food processor. Turn the processor on and after about 20 seconds, add in cold water, 1 Tbsp. at a time, until dough comes together in larger chunks. Turn processor off and take dough out. Form dough into a ball, press down into a disk shape, then wrap with plastic and chill for 30 minutes.
Combine blackberries, blueberries, lemon zest, juice, honey, sugar, and cornstarch in a medium size bowl. Toss to combine until berries are evenly coated. Set aside.Slice brie into ¼ inch pieces. Set aside.
Line a sheet tray with parchment paper. Unwrap dough and roll out on a floured surface. Roll to about 16” diameter, or about 1/8”thickness. Roll dough onto rolling pin, then out onto sheet tray with parchment. Place slices of brie in the center of the dough, leaving about 3”around clean. Top brie with berry mixture. Take the sides of dough and fold on top over the berries. Place sheet tray in freezer to chill the dough before baking. Freeze for 5 minutes.
Preheat oven to 425 degrees Fahrenheit. Mix egg wash together by whisking an egg with water in a small bowl.
Take galette out of the freezer, then brush egg wash over the surface of the dough. Bake for 30 minutes, or until evenly golden brown.
Let galette cool for 20 minutes at room temperature, then slice and serve!