In a medium saucepan, melt the butter over medium heat. Continue to cook, stirring frequently, until the butter turns a light golden brown and develops a nutty aroma. Remove from heat and let it cool slightly.
In a large mixing bowl, whisk together the flour and baking soda. Set aside.
In another bowl, combine the brown butter, granulated sugar, and brown sugar. Beat until well combined and smooth.
Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract until fully incorporated.
Gradually add the flour mixture to the wet ingredients, mixing until just combined. Be careful not to overmix.
Gently fold in the chopped Heath bars until evenly distributed throughout the dough.
Cover the dough with plastic wrap and chill in the refrigerator for at least 30 minutes.
Preheat your oven to 350°F (175°C). Line your baking sheets with parchment paper.
Using a cookie scoop or tablespoon, drop rounded dough balls onto the prepared baking sheets, leaving space between each cookie. Bake for 10-12 minutes, or until the edges are golden and the centers are set.
Remove the cookies from the oven and let them cool on the baking sheets for a few minutes before transferring them to a cooling rack. Allow them to cool completely, and then enjoy your scrumptious Brown Butter Toffee Cookies!