Melt butter in a saucepan over medium heat, stirring constantly until it foams, turns golden brown, and develops a nutty aroma; transfer to a heat-proof bowl to cool for 15 minutes.

In a medium bowl, whisk together the flour, baking soda, and sea salt until combined.

In a large mixing bowl, combine the cooled browned butter with granulated sugar and brown sugar, mixing until well incorporated.

Add the whole egg, egg yolk, and vanilla extract to the butter mixture, whisking until the batter is light and smooth.

Gradually fold the dry flour mixture into the wet ingredients using a spatula until no dry streaks remain.

Stir in the dark chocolate chunks and toffee bits until evenly distributed throughout the dough.

Cover the bowl and refrigerate the dough for at least 2 hours to develop flavor and improve texture.

Preheat oven to 350°F (175°C) and line baking sheets with parchment paper or silicone mats.

Scoop 2-tablespoon sized mounds of dough onto the prepared sheets, spacing them 2 inches apart.

Bake for 10 to 12 minutes or until the edges are golden brown while the centers remain slightly soft.

Remove from the oven and immediately sprinkle each cookie with a pinch of flaky sea salt before cooling on the pan for 5 minutes.