Brown the butter by melting unsalted butter in a medium saucepan over medium heat until golden brown with a nutty aroma, about 5-7 minutes. Cool and refrigerate to solidify for about 20 minutes.

Mix chilled brown butter with granulated sugar and brown sugar using a stand mixer until light and fluffy, around 3-4 minutes. Add in the egg and vanilla extract, mixing until smooth.

Combine dry ingredients: all-purpose flour, baking powder, baking soda, and salt in a separate bowl. Gradually add this to the wet ingredients on low speed until just combined.

Fold in Heath toffee bits into the dough with a spatula until evenly distributed.

Scoop dough into balls (about 2 tablespoons each), place on a plate or baking sheet, cover with plastic wrap, and refrigerate for at least 2 hours.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

Bake cookie dough balls spaced 2 inches apart for 11-13 minutes until edges are golden brown and centers are soft.

Cool cookies on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.