Melt the butter in a medium stainless steel sauté pan over medium heat, swirling occasionally.
Continue cooking until the butter becomes foamy with crackling sounds, then swirl or stir until it smells nutty and brown bits form.
Remove from heat and pour the browned butter, including the brown bits, into a mixing bowl.
Stir in the granulated sugar and dark brown sugar into the hot butter mixture and set aside to cool to room temperature.
In a medium bowl, whisk together the all-purpose flour, bread flour, baking soda, baking powder, salt, and espresso powder if using.
Whisk eggs, yolk, and vanilla into the cooled butter mixture until combined.
Gradually fold the flour mixture into the butter mixture using a rubber spatula.
Stir in the chopped semisweet chocolate and toffee bits.
Wrap the dough in plastic wrap and refrigerate for at least 24 hours and up to 72 hours.
Remove the dough from the refrigerator and let it soften at room temperature for about 1 hour to make scooping easier.
Preheat oven to 350°F and line baking sheets with parchment paper.
Portion the dough into 3-tablespoon balls using a large cookie scoop and place on prepared baking sheets.
Optionally, freeze dough balls solid on a baking sheet, then store frozen in an airtight container for up to 6 weeks.
Bake cookies for 12 to 14 minutes until golden brown.
Remove cookies from oven and immediately sprinkle with flaky sea salt, if desired.
Let cookies cool on the tray for 2 minutes before transferring to wire racks to cool completely.
Store cooled cookies in an airtight container at room temperature for up to 3 days.