Preheat oven to 350°F. Line baking sheets with parchment paper using non-stick technique.
Melt 3/4 cup butter in a saucepan over medium heat. Stir constantly until golden brown and nutty. Cool 5 minutes.
Add melted butter to a mixing bowl, then add 1 cup brown sugar and 1/3 cup white sugar. Beat on medium speed for 2-3 minutes until emulsified.
Add 1 egg, its yolk from another, and 1 tsp vanilla. Mix for 1 minute.
In a separate bowl, whisk 1 3/4 cups flour, 1/4 cup espresso powder, 1/2 tsp baking soda, and 1/2 tsp salt until espresso powder dissolves.
Add dry ingredients to wet mixture. Mix on low speed until just combined.
Fold in chopped dark chocolate gently using a silicone spatula. Freeze dough for 20 minutes to firm it for cleaner edges.
Portion 1 oz dough balls onto prepared sheets. Bake for 11 minutes or until edges are set but centers remain soft.
Cool on sheets for 5 minutes before transferring to a wire rack.