Cookies: Put an oven rack in the center of the oven. Preheat the oven to 325 degrees F. Line 2 baking sheets with parchment paper or silicone mats. Set aside.
In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt. Using an electric stand mixer fitted with a paddle attachment, beat the butter and sugars together until fluffy. Beat in the egg and vanilla. With the machine running, gradually add the flour mixture until just blended. Stir in the chocolate chips. Using a 1-ounce ice cream or cookie scoop, form 12 equal-sized pieces of dough onto each baking sheet. With damp hands, form the dough into balls. Flatten the tops of the dough slightly and bake until the tops of the cookies begin to crack slightly, about 14 minutes. Cool for 5 minutes. Transfer the cookies to a wire rack to cool completely, about 20 minutes.
Filling: In a medium bowl, using an electric mixer, beat the cream cheese and vanilla together until fluffy. Gradually add the powdered sugar and mix until smooth. Color the frosting by mixing in the food coloring, 1 drop of at a time, until the desired color is reached. Add water, if needed, 1/2 teaspoon at a time, to make the consistency spreadable.
Spread the frosting on the flat side of half of the cookies and put the remaining cookies on top. Refrigerate for 30 minutes to allow the filling to stiffen slightly. Serve at room temperature.