In a medium saucepan over medium heat, melt the butter slowly while stirring constantly until it turns golden brown and develops a nutty aroma. Transfer the butter into a bowl and stir in the espresso powder. Let it cool in the refrigerator until it firms up, about 1–2 hours.
Beat together the solidified browned butter and both sugars on medium-high speed for about 3–4 minutes until light and fluffy.
Add one large egg and half a tablespoon of vanilla extract. Beat until smooth.
Mix in baking powder, baking soda, salt, and flour into the mixture on low speed just until combined.
Gently fold in the Heath toffee bits using a spatula until evenly distributed.
Scoop out large balls of dough onto parchment-lined baking sheets. Refrigerate them for several hours or up to 24 hours.
Preheat your oven to 350°F (175°C). Place your chilled dough balls on another parchment-lined baking sheet. Sprinkle each cookie with flaked sea salt before baking for about 11–13 minutes until edges are golden brown.
Allow your cookies to cool slightly on the baking sheet before transferring them to a wire rack to cool completely.