Preheat oven to 375℉. Line 2 baking sheets with parchment paper and set aside.
Cook butter in a medium saucepan over medium heat, stirring often, until it foams and then browns, 5–8 minutes. Let cool slightly.
Meanwhile whisk flour, baking soda, and kosher salt in a medium bowl.
To the bowl of an electric mixer, add brown sugar, granulated sugar and cooled browned butter. Beat on medium until incorporated. Add egg, egg yolk and vanilla and beat well. Scrape the bowl. Reduce mixer speed to low and add dry ingredients, mixing until just combined. Mix in toffee and chocolate chips by hand or briefly with the electric mixer.
Using a mini ice cream scoop, place dough balls on the parchment-lined baking sheet, spacing about 2" apart. Sprinkle with sea salt.
Bake cookies until edges are golden brown and firm but centers are still soft, about 9 minutes. They should look slightly underbaked in the center. Let cool on baking sheets for 5-10 minutes until set and slightly cooled then transfer to a wire rack and let cool completely.