Preheat the oven to 350° F. Line 2 baking sheets with parchment paper.

In a mixing bowl, beat together the butter, brown sugar, espresso powder, and vanilla until light and fluffy, about 3-5 minutes. Add the egg, mixing to combine. Then, add the maple and mix to combine. Add the flour, baking soda, salt, cinnamon, ginger, cardamom, nutmeg, all-spice, and pepper, beating until combined.

Place the sugar in a small bowl.

Roll the dough into tablespoon-size balls (if the dough is too sticky, add 2-4 additional tablespoons flour), then lightly roll through the sugar. Place on the prepared baking sheet, spacing the cookies 2 inches apart. Bake for 8-10 minutes or until the cookies are just starting to set around the edges. The centers should be a little doughy. Let cool on the pan.

Meanwhile, make the icing. Add the butter to a pot set over medium heat. Allow the butter to brown lightly until it smells toasted, about 2-3 minutes. Remove from the heat. Let cool 5 minutes. Whisk in the powdered sugar, milk, vanilla, and salt. Immediately spread the icing over the cookies, it will set quickly. Sprinkle with sea salt. Store in an airtight container for up to 5 days.