Slice butter into pieces. In a medium saucepan over low to medium heat melt the butter down. Continue to cook, stirring often, for eight to ten minutes. Brown bits will appear at the bottom and it will become fragrant. Pour into a heatproof bowl and set aside for 10 minutes.
After 10 minutes, add browned butter, brown sugar, and granulated sugar to the bowl of a stand mixer using the paddle attachment or using a hand mixer. Combine on medium speed for one to two minutes.
Add egg, egg yolk, and vanilla extract and mix on medium speed for another two minutes. In a separate bowl whisk together the flour, old fashioned rolled oats, baking soda, and salt. Add to the wet ingredients. Mix on the lowest speed just until combined, about 30 seconds.
Add the chopped chocolate and toffee. Mix on the lowest speed for about 10 to 15 seconds, just until combined. Scoop cookie dough into balls using a cookie scoop or a 1/4 cup measuring cup. Press extra pieces of toffee and chocolate chunks on top of the cookie balls. Set uncovered in the refrigerator for 30 minutes while you preheat the oven to 350°
After 30 minutes bake in the middle rack of preheated oven 1-2 inches apart for 11-14 minutes. The middles will appear set and the edges will be just slightly golden brown. Sprinkle with flaky sea salt if desired.
Allow to cool on cookie sheet for about five minutes and then place on a wire rack to cool completely.
Notes
Store cookies in an airtight container for two to three days at room temperature.
Keyword brown butter, Chocolate chip cookies, Cookies, oatmeal cookies, toffee