Preheat your oven to 350°F and line a cookie sheet with parchment paper.
In a large bowl, combine the chocolate cake mix, eggs, and vegetable oil. Stir until the mixture is well blended. The dough will be thick.
Use a cookie scoop or a heaping tablespoon to drop ball-shaped portions onto the prepared cookie sheet, spacing them about 2 inches apart.
Place the cookie sheet in the oven and bake for 7 to 8 minutes or until the cookies are just set. Remove the cookies from the oven and let them cool on the sheet for about 5 minutes.
While the cookies are cooling, melt the butter in a small saucepan over medium heat. Add the unsweetened cocoa powder, milk, and vanilla, whisking until the mixture is smooth.
Remove from heat and stir in the powdered sugar until the icing is completely smooth. If the frosting is too thick to drizzle, add another splash of milk to thin it. Drizzle the frosting evenly over the warm cookies and let it set before serving.