Line a baking sheet with parchment paper, set aside. Combine butter and sugar in a large saucepan over medium-high heat. Stir constantly until butter is melted, about 5 minutes. Once the butter is melted, stop stirring and bring to a boil. Once boiling, cook, stirring occasionally, until it turns a dark amber color and the temperature reaches 285 degrees F, 20 to 30 minutes.
Carefully pour onto the prepared baking sheet. Sprinkle with coarse sea salt and allow to cool completely. Once cool, use your hands or a food processor to crush the toffee into small chunks. Alternatively you could use store bought toffee bits.
For the cookie dough:
In the bowl of a stand or hand mixer fitted with a paddle attachment, cream the butter and sugars together until creamy, about 3-4 minutes. Add in the vanilla extract, whole egg, and the egg yolk. Mix until incorporated.
In a medium mixing bowl combine the flour, baking soda, baking powder, and salt. Slowly add the dry ingredients into the wet ingredients, mix on low until fully combined. Fold in the chocolate chips and the crushed toffee bits. Cover the dough and allow to chill for 60 minutes.
Preheat oven to 350 degrees F, line a baking sheet with parchment paper, set aside.
Once cooled, use a portion scoop to measure even sized scoops of dough (roughly 1 oz.) and transfer to the prepared baking sheet, leaving 3-4 inches between each cookie - these will spread*. Bake at 350 for 10-12 minutes until golden brown. Allow to cool slightly on the baking sheet then transfer to a wire rack to finish cooling. Store in an airtight container for up to a week!
Notes
*You can also substitute store-bought toffee, you will need about 1 cup.*Toffee can also be made ahead of time.*These cookies will spread, if desired after baking, while still warm use a round cookie cutter or jar lid to gently scoot the cookies into perfect circles! I only put about 4 or 5 cookies on a half sheet pan at a time.