Brown the Butter: In a medium saucepan over medium heat, melt the butter and continue cooking it beyond the boiling and foaming stages, stirring frequently, until it becomes golden brown and emits a nutty aroma. Carefully monitor to avoid burning. Once browned, pour the butter—along with all the flavorful brown bits—into a glass bowl. Immediately stir in the espresso powder until fully dissolved. Refrigerate the mixture until it reaches a soft, solid consistency, about 1 to 2 hours.
Make the Dough: Using a stand mixer fitted with the paddle attachment, combine the solidified brown butter with both the brown and granulated sugars. Beat on medium-high speed for 3 to 4 minutes, or until the mixture is light and fluffy.
Add the Egg and Vanilla: Lower the mixer speed and add the egg, beating until smooth, about 30 seconds. Then add the vanilla extract and mix until fully incorporated.
Mix in the Dry Ingredients: Add the baking powder, baking soda, salt, and flour to the bowl. Mix on low speed just until the dry ingredients are incorporated. It's okay if a few streaks of flour remain—avoid overmixing the dough.
Stir in the Toffee Bits: Gently fold in the toffee bits by hand, ensuring they are evenly distributed throughout the dough.
Chill the Dough: Scoop the dough into large balls using a ¼ cup cookie scoop. Arrange them on a baking sheet and refrigerate for several hours—ideally 24 hours—to enhance the flavor and reduce spreading during baking.
Preheat the Oven: When ready to bake, preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
Bake the Cookies: Place up to 8 dough balls on the prepared baking sheet, leaving enough space between each. Sprinkle a pinch of flaked sea salt on top of each cookie. Bake for 11 to 13 minutes, or until the edges are golden and the centers are just set.
Cool and Enjoy: Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely. Serve warm or at room temperature, ideally with a cup of coffee for the ultimate treat.