Place the butter in a light-colored saucepan over medium heat. Stir frequently as it melts, foams, and turns golden brown with nutty-smelling brown specks at the bottom, about 5 to 7 minutes. Pour immediately into a large heatproof bowl and let cool for 15 minutes.
In a medium bowl, whisk together gluten free all-purpose flour blend, baking soda, cornstarch, and salt. Set aside.
Add the brown sugar and granulated sugar to the cooled brown butter and whisk until smooth and combined. Whisk in the egg, egg yolk, and vanilla extract until the mixture is thick and slightly glossy.
Add the flour mixture and stir with a spatula until no dry streaks remain. Fold in the toffee bits and chocolate chips until evenly distributed. Cover the bowl and refrigerate for at least 1 hour.
Preheat your oven to 350 degrees F and line two baking sheets with parchment paper. Scoop about 2 tablespoons of dough, roll into balls, and place 3 inches apart on the prepared baking sheets.
Bake for 11 to 13 minutes until the edges are golden brown but the centers still look slightly underdone and puffy. Immediately sprinkle each cookie with a small pinch of flaky sea salt.
Let the cookies cool on the baking sheet for 10 minutes before transferring to a wire rack. They will flatten slightly and develop chewy centers with crisp, toffee-studded edges as they cool.