In a medium saucepan, melt the butter over medium heat until golden brown and fragrant, stirring frequently. Remove from heat and let cool.
In a large bowl, whisk together the browned butter, brown sugar, and granulated sugar until smooth.
Add eggs one at a time, mixing well after each addition, followed by the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the toffee bits and chocolate chips.
Chill the dough in the refrigerator for at least 30 minutes.
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
Scoop dough into balls and place them onto the prepared baking sheets, spacing them 2 inches apart.
Bake for 10-12 minutes or until edges are lightly golden and centers are set.
Let cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.