Preheat the oven to 375 degrees F. Line 2 baking sheets with parchment.
In a large bowl, whisk the flour, brown sugar, baking powder, baking soda and salt to combine. Add the butter and toss with the flour until each piece is separated and fully coated in flour.
Use your hands or a pastry cutter to cut the butter into the flour mixture until the mixture resembles a coarse meal (there should still be a few small crumbly bits of butter). Make a well in the center of the bowl.
In a large liquid measuring cup, whisk the buttermilk, egg and vanilla together to combine. Pour into the well in the center of the bowl, then stir with a rubber spatula to combine. The dough should come together and be slightly sticky--if it seems dry, add more buttermilk, 1 tablespoon at a time, until it comes to the right consistency.
Add the chocolate and stir until uniformly combined. Use a 1/4-cup scoop to drop heaping mounds of the batter on the prepared baking sheets, staggering the biscuits and placing 6 per sheet. Sprinkle each biscuit with turbinado sugar.
Bake until the biscuits are golden brown spring back slightly when pressed in the center, 15 to 18 minutes. Let cool at least 15 minutes on the baking sheets and serve warm, or cool completely before serving.