In a saucepan, melt the butter over medium heat, stirring frequently until it turns golden brown and has a nutty aroma.

In a mixing bowl, whisk together the flour, baking soda, and salt.

In another bowl, combine the browned butter, brown sugar, and granulated sugar. Mix until smooth. Add the egg and vanilla extract, and mix until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in the toffee bits.

Preheat the oven to 350°F (175°C). Drop spoonfuls of dough onto a baking sheet lined with parchment paper. Bake for 10-12 minutes or until the edges are golden.

Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.