Preheat the oven to 350 degrees. Prepare a large baking sheet with parchment paper.
Beat the butter at medium speed until fluffy. Slowly add the sugar, scraping the bowl down as needed. Add the egg, millk, and vanilla, blending until well mixed.
Sift together the flour, cocoa, and salt. Add the flour mixture to the butter mixture and beat until combined. Refrigerate the cookie dough for at least one hour.
Using a small (about 1 tablespoon) cookie scoop, place the cookie dough at least 1 inch apart. Bake for 10 to 13 minutes.
When the cookies are done, remove from the oven and gently press the back of a teaspoon into the center of each cookie. Allow the cookies to cool on the baking sheet.
Meanwhile, place the dark chocolate chips, cream, and butter in a microwaveable bowl. Heat in the microwave, stirring every 30 seconds until smooth.
Spoon a small amount of the chocolate into the hole in each cookie and immediately place a cherry in the center. Allow the chocolate to set completely before serving.