Cream together browned butter and sugar until pale and fluffy.
Add egg and vanilla extract and mix until combined.
Add salt and baking soda. Mix until well combined, making sure to scrape down the sides and bottom of the bowl.
Mix in flour until just combined. Fold in toffee bits.
Scoop 2 tbsp (#40 cookie scoop) balls of dough onto a prepared baking sheet.
Bake for 10 minutes, or until edges are lightly browned. Allow to cool on baking sheet for 2-3 minutes before transferring to a wire rack to cool completely.
Notes
*You can use store-bought or homemade toffee bits. I love using my homemade version, here: http://brooksidekitchen.com/easy-homemade-toffee-bitsIf you'd like more information on how to brown butter, I have a post on it, here: http://brooksidekitchen.com/how-to-brown-butterTip for Round Cookies - Since the toffee bits melt and spread in the oven, the cookies may come out in unique, less-than-round, shapes. To create a more uniform cookie, first bake them as written above. Once you remove them from the oven, while they're still warm, take a round metal cookie cutter (larger than the size of the final cookie) and use it to gently pull in the sides of the cookie that extend outside of the cutter. Once all parts of the cookie fit within the cutter, place the cookie cutter around the cookie and move it around in a circular motion to help the cookie form a round shape. Allow the cookies to cool on the pan for 2-3 minutes before transferring to a wire rack to cool completely.