In a medium saucepan, melt the unsalted butter over medium heat, stirring frequently until it turns golden brown, about 5-7 minutes. Let it cool for 10-15 minutes.

In a large mixing bowl, combine the cooled brown butter with brown sugar and granulated sugar. Mix until smooth and creamy, about 2 minutes. Add vanilla extract and egg, mixing until well combined.

In a separate bowl, whisk together flour, baking soda, and salt. Ensure the dry ingredients are evenly distributed.

Gradually pour the dry mixture into the wet ingredients, mixing gently until just combined. The dough should be slightly sticky but not wet.

Fold in the toffee bits and chocolate chips, ensuring they are evenly distributed throughout the dough.

Cover the dough with plastic wrap and refrigerate for at least 1 hour, or up to overnight.

Preheat your oven to 350°F (175°C). Scoop tablespoon-sized portions onto lined baking sheets, spacing them about 2 inches apart. Bake for 10-12 minutes until the edges are golden brown and centers remain soft.

Let the cookies cool on the tray for 5 minutes before transferring to a wire rack. Optionally, sprinkle with flaky sea salt before baking.