Whisk flour, finely ground coffee beans, baking soda, and salt in a bowl until combined. Set aside.
In a large bowl using a hand-held or stand mixer fitted with a paddle attachment, beat mascarpone, butter, granulated sugar, and brown sugar on medium speed until fluffy and light in color, about two minutes. Add in egg and vanilla. Beat until incorporated.
With the mixer running on low speed, slowly add in dry ingredients. Beat on low just until the flour has combined, scraping down the sides of the mixer as needed. The dough will be sticky. Remove bowl from the stand mixer, and add in ¾ cup of milk chocolate morsels. Stir chocolate morsels into the dough with a silicone spatula.
Scoop cookies into 3 tablespoon balls and place on a parchment lined baking sheet. Using 1 ¾ cups of milk chocolate morsels, cover the outside of each cookie dough scoop. Place in the freezer for 30 minutes until the dough has firmed up.
Heat oven to 350°F (175°C).
Remove cookies from the freezer and place 3 inches (8 centimeters) apart on a parchment lined baking sheet. Bake the cookies for 15-20 minutes until golden brown around the edges and the middle of the cookie has set. Once out of the oven, use the remaining ½ cup of milk chocolate morsels to fill in bare spots on top of the cookie. Allow to cool for 5 minutes on the baking sheet, then transfer to a cooling rack to cool completely.
Store cookies in a single layer in an airtight container at room temperature for up to 5 days.