Melt the butter in a medium saucepan over medium heat. Stir constantly as it crackles and foams. Once the crackling stops and golden brown specks appear at the bottom with a nutty aroma, immediately remove from heat. Pour the browned butter (including the specks) into a large heat-proof bowl and let cool for 15-20 minutes.

Once the butter has cooled slightly but is still liquid, whisk in the dark brown sugar and granulated sugar until well combined. Add the egg, egg yolk, and vanilla extract. Whisk vigorously for about 1 minute until the mixture is smooth, pale, and ribbons off the whisk.

In a separate medium bowl, whisk together the all-purpose flour, instant espresso powder, baking soda, and kosher salt.

Pour the dry ingredients into the wet ingredients. Use a rubber spatula to gently fold them together until just a few flour streaks remain.

Add the toffee bits and chocolate chunks to the dough. Fold gently until evenly distributed and no dry flour remains. Do not overmix.

Cover the bowl tightly with plastic wrap and chill the dough in the refrigerator for at least 1 hour (or overnight for best results).

Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper.

Using a large cookie scoop (about 3 tablespoons), portion the chilled dough into balls. Place them on the prepared baking sheets, spacing them about 2 inches apart.

Bake one sheet at a time in the center of the oven for 10-12 minutes. The edges should be set and golden, but the centers should still look slightly underbaked.

Remove from the oven and immediately sprinkle generously with flaky sea salt. Let the cookies cool on the baking sheet for 10 minutes before transferring them to a wire rack to cool completely.