Brown the butter: In a light-colored saucepan over medium heat, melt the butter and cook, stirring, until it foams and the milk solids turn golden and smell nutty, 3–5 minutes. Scrape into a large mixing bowl and cool until just warm, about 10 minutes.
Whisk the dry ingredients: In a separate bowl, whisk almond flour, baking soda, fine sea salt, and espresso powder until evenly combined.
Make the wet base: To the cooled brown butter, whisk in the brown sugar for about 1 minute until glossy. Whisk in the vanilla, almond extract, and egg until smooth.
Combine: Switch to a spatula and fold the dry mixture into the wet until no dry spots remain. Stir in 3/4 cup chocolate chips just until dispersed.
Rest the dough for 15 minutes to let the almond flour hydrate; the dough will thicken slightly.
While the dough rests, heat the oven to 360°F (182°C) and line 2 baking sheets with parchment paper.
Portion and quick-chill: Scoop dough into 1.5-tablespoon mounds (about 30 g each) spaced 2 inches apart. Press a few extra chips on top of each. Freeze the tray for 10 minutes (or refrigerate 20 minutes) to reduce spread.
Bake 9–11 minutes, rotating the pan halfway, until edges are lightly golden and centers look just set. Immediately sprinkle with flaky sea salt, if using.
Cool on the sheet for 5 minutes, then transfer to a rack to cool completely. Cookies firm up as they cool.