Brown the butter: In a light-colored saucepan, melt butter over medium heat. Continue cooking, swirling often, until it foams, sizzles, and then quiets down. Watch for nutty-smelling, golden-brown specks to form at the bottom (5-8 min).

Cool the butter: Immediately pour the brown butter (including the brown bits) into a large, heatproof bowl. Let cool for 15-20 minutes.

Combine dry ingredients: In a medium bowl, whisk together the flour, baking soda, cornstarch, and salt.

Mix wet ingredients: To the cooled brown butter, whisk in the brown sugar and granulated sugar until smooth. Add the egg, egg yolk, and vanilla, and whisk until glossy.

Combine mixtures: Add the dry ingredients to the wet ingredients and fold with a spatula until just combined. Do not overmix. Fold in the toffee bits.

Chill the dough: Press plastic wrap onto the surface of the dough and refrigerate for at least 2 hours, or overnight. This step is mandatory for thick cookies.

Preheat and prep: Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

Scoop: Use a 1.5-tablespoon cookie scoop to make dough balls. Place 2-3 inches apart on the prepared baking sheets.

Bake: Bake for 10-12 minutes, until edges are golden but centers look slightly soft and underdone.

Finish: Immediately sprinkle each hot cookie with a small pinch of flaky sea salt. Let cool on the pan for 5 minutes before transferring to a wire rack.