Brown the butter: Add the butter to a light-colored saucepan over medium heat. Cook, stirring, until the milk solids turn deep golden and smell nutty, 5–7 minutes. Immediately scrape the butter and browned bits into a large mixing bowl and let cool until just warm to the touch, about 10 minutes.
While the butter cools, heat the oven to 365°F (185°C) and line two baking sheets with parchment paper.
Whisk the dry ingredients: In a medium bowl, whisk together the gluten-free flour, baking soda, fine sea salt, and espresso powder (if using).
Build the wet base: To the cooled brown butter, whisk in the brown sugar and granulated sugar until it looks sandy. Add the egg and whisk vigorously for 30–45 seconds until glossy and slightly thickened. Whisk in the vanilla and milk.
Combine: Switch to a spatula and fold the dry mixture into the wet just until no dry streaks remain. Stir in about three-quarters of the chocolate chips, reserving the rest for topping.
Rest the dough: Cover and chill the bowl for 15 minutes to help the gluten-free flour hydrate and the dough firm slightly for easier scooping.
Scoop and top: Using a 1.5-tablespoon scoop (about 30g), portion dough onto the prepared sheets, spacing 2 inches apart. Lightly flatten each mound and dot the tops with the remaining chocolate chips.
Bake: Bake one sheet at a time for 9–11 minutes, rotating the pan once at the 7-minute mark, until edges are set and centers look slightly pale and soft. For extra crinkles, rap the pan once on the rack right after baking.
Cool: Let cookies rest on the sheet for 5 minutes, then transfer to a wire rack to cool completely. Repeat with remaining dough.