Preheat the oven to 350°F.
Line baking sheets with parchment paper or silicone baking mats.
In a medium bowl, whisk together the flour, espresso powder, baking soda, and salt.
In a large bowl, use an electric mixer to beat the butter and sugars on medium-high speed until well combined and smooth, about 1 to 2 minutes. Add the milk, egg, egg yolk, and vanilla and beat until combined. On low speed, gradually add the flour mixture and beat until just combined.
Using a spoon or spring-loaded scoop, drop 2 tablespoon–sized balls of dough onto pre- pared baking sheets.
Bake for about 10 minutes, or until the edges are slightly browned. Let cool on baking sheets for 5 minutes before removing to wire racks to cool completely. Freeze the cookies until frozen, at least 1 hour. Cookies can be stored in airtight containers in the freezer for up to 1 month.