Preheat the oven to 350F degrees and line two cookie sheets with parchment paper or silicone baking mats. If you plan to chill your cookie dough, you'll do this step prior to baking instead.
In a medium-sized saucepan over medium heat, melt the butter. After the butter melts, begin to gently stir it using a rubber spatula or whisk. The butter will begin to bubble and make popping noises and after a few minutes you'll notice small brown flecks forming. It will then start to give off a nutty aroma and will look light brown in color due to the brown flecks forming. Remove the sauce pan from the heat and pour the browned butter into a bowl to cool for 10 minutes.
Once the butter had cooled down so it's no longer scalding, beat together the browned butter and sugars in a large bowl using an electric mixer on medium speed (about 30 seconds). Then add in the egg, extra egg yolk and vanilla and continue beating until evenly combined (about 30 more seconds). Turn the mixer off and add in the flour, baking soda and salt. Then turn the mixer back on to low speed and slowly beat until combined. Turn off the mixer and stir in the toffee bits and chocolate chips using a large wooden spoon or rubber spatula.
Using a cookie scoop or tablespoon, form the dough into balls about 2 to 3 tablespoons in size. Do not flatten your cookie dough balls. I got 20 cookies total. If baking immediately, place the cookies 2 inches apart on your lined sheets and bake for 9-11 minutes or until the tops look almost done. Allow the cookies to cool for at least 10 minutes on the cookie sheet, and place a few extra chocolate chips on the top of each cookies.
If chilling the dough, place the cookie dough balls on a plate, and cover with clingfilm. Chill in the refrigerator for 30 minutes or up to 2 days. When ready to bake, remove the cookie dough balls from the fridge then preheat the oven to 350F degrees. Line 2 cookie sheets with parchment paper or silicone baking mats, place the cookies 2 inches apart on your lined sheets and bake for 9-11 minutes or until the tops look almost done. Allow the cookies to cool for at least 10 minutes on the cookie sheet, and place a few extra chocolate chips on the top of each cookie.