Place ½ of the butter into a medium saucepan over medium heat. Let the butter cook while occasionally stirring to ensure the butter is cooking evenly.
½ cup butter
Cook the butter until it is a deep golden brown color and smells nutty and toasted, about 5 -7 minutes. Remove the pan from the heat. Let the butter cool to room temperature.
In a medium bowl, whisk together the flour, instant espresso, baking soda, and salt. Set aside.
2 ¼ cups all purpose flour, 1 tablespoon instant espresso powder, 1 teaspoon fine sea salt, 1 teaspoon baking soda
In the bowl of a stand mixer fitted with the paddle attachment, cream the remaining ½ cup of butter, brown sugar and granulated sugar until light and fluffy, about 5 minutes.
½ cup butter, room temperature, 1 cup light brown sugar, ⅓ cup granulated sugar
Beat in the vanilla and the cooled brown butter until light and creamy about 2 minutes.
2 teaspoons pure vanilla extract
Beat in the egg and the egg yolk and beat for another minute.
1 large egg, 1 large egg yolk
On low speed, add the flour mixture, beating just until incorporated.
Remove the bowl from the mixer. Give the dough one final stir to ensure the flour is incorporated. Use a spatula to fold in the chocolate and toffee.
1½ cups bittersweet chocolate, coarsely chopped, ¾ cup toffee bits
Scoop the dough with a medium size/2 tablespoon cookie scoop onto two lined cookie sheets. Chill the dough for at least 30 minutes but overnight is better.
While the cookie dough chills, preheat the oven to 350F.
Sprinkle the cookie dough scoops with a pinch of flaky salt. Bake 14-16 minutes, or until the cookies begin to brown around the edges, and the centers look set. Don't over bake.
flaky salt, for sprinkling
Let the cookies cool 10 minutes on the parchment before placing the cookies on a cooling rack to cool completely.