In a medium stainless steel sauté pan over medium heat, melt the butter. Continue cooking, gently swirling the pan from time to time. The butter will start to foam and make popping and crackling sounds. When the sounds begin to subside, keep swirling or stir constantly—watch for the butter to take on a nutty aroma and for browned bits to form on the bottom of the pan. Once those bits turn a deep amber color, immediately remove the pan from the heat and pour the butter into a mixing bowl, making sure to scrape in all the flavorful browned bits from the bottom.
Add the granulated sugar and dark brown sugar to the warm browned butter and stir to combine. Set the mixture aside to cool to room temperature.
In a separate medium bowl, whisk together the all-purpose flour, bread flour, baking soda, baking powder, fine sea salt, and espresso powder (if using).
Once the butter mixture has cooled, whisk in the eggs, egg yolk, and vanilla extract until the mixture is fully blended. Using a rubber spatula, gradually mix in the dry ingredients until just combined. Fold in the chopped semisweet chocolate and toffee bits. Wrap the dough tightly in plastic wrap and refrigerate for at least 24 hours and up to 72 hours for optimal flavor and texture.
Before baking, let the dough sit at room temperature for about 1 hour, or until it softens slightly and is scoopable.
Preheat the oven to 350ºF (175ºC) and line baking sheets with parchment paper.
Scoop the dough into 3-tablespoon portions using a large cookie scoop and place onto the prepared baking sheets. The dough may be a bit firm and require effort to scoop.
If desired, you can portion the dough and freeze the balls on a baking sheet until solid. Once frozen, transfer them to an airtight container and freeze for up to 6 weeks.
Bake the cookies for 12 to 14 minutes, or until the edges are golden and the centers are just set. Remove from the oven and, if desired, sprinkle with flaky sea salt. Let the cookies rest on the baking sheet for 2 minutes before transferring them to a wire rack to cool completely.
Store cooled cookies in an airtight container at room temperature for up to 3 days.