In a medium stainless steel sauté pan set over medium heat, melt the butter. Swirling the pan occasionally, continue to cook the butter until it develops a nutty aroma and brown bits start to form. Remove from heat and pour into a mixing bowl, keeping the brown bits.
Add the granulated sugar and brown sugar to the hot butter, stirring to combine, and set aside to cool to room temperature.
In a medium bowl, combine the flours, baking soda, baking powder, salt, and espresso powder.
To the cooled butter mixture, whisk in the eggs, yolk, and vanilla until combined. Gradually stir in the flour mixture with a rubber spatula. Stir in the chocolate chunks and toffee bits. Wrap dough in plastic wrap and refrigerate for at least 24 hours but no more than 72 hours.
Let dough sit at room temperature just until it is soft enough to scoop, about 1 hour.
Preheat the oven to 350ºF. Line baking sheets with parchment paper.
Divide the dough into 3-tablespoon sized balls using a large cookie scoop and drop onto prepared baking sheets.
Optionally, you can portion the dough, place it on a baking sheet, and freeze just until solid. Remove frozen balls of dough to an airtight container and store for up to 6 weeks.
Bake for 12 to 14 minutes, or until golden brown. Remove from oven and sprinkle flaky sea salt on top of the cookies, if desired. Let cookies cool for 2 minutes before moving to wire racks to cool completely.
Store in an airtight container at room temperature for up to 3 days.