Preheat your oven to 350°F and line a baking sheet with parchment paper. While the oven heats, sift together the flour, cocoa powder, baking soda, baking powder, and salt in a medium bowl—sifting removes lumps and aerates the dry ingredients for a smoother batter. Set this dry mixture aside. Ensure your butter for the dough is at room temperature (about 70°F) so it creams properly with the sugar.
Beat the 1/2 cup + 1 tbsp room-temperature butter and sugar together for 2-3 minutes until light and fluffy—this incorporation of air helps the cookies rise and gives them a tender crumb. Add the egg and beat until fully combined, then stir in the vanilla essence and red food coloring until the mixture is evenly colored. Gently fold in the dry ingredient mixture from Step 1 until just combined; avoid overmixing, which can make cookies tough.
Using a cookie scoop or your hands, shape the dough from Step 2 into 1-inch balls and place them about 2 inches apart on your prepared baking sheet. Gently flatten each ball with the bottom of a glass or your palm to about 1/4-inch thickness. Bake for 10-11 minutes until the edges are just set but the centers still have a slight give—the cookies will firm up as they cool.
Let the baked cookies cool on the baking sheet for 5 minutes to firm up slightly, then transfer them to a wire cooling rack for about 30 minutes until completely cooled. I find that this two-stage cooling prevents them from breaking apart while still allowing air circulation for even cooling.
While the cookies cool, beat the softened cream cheese and 1/4 cup room-temperature butter together until smooth and creamy—this usually takes about 1-2 minutes. I always use Philadelphia brand cream cheese for the best consistency and flavor. Gradually add the powdered sugar, vanilla essence, and salt, then beat for another 2 minutes until light and fluffy. The frosting should be spreadable but hold its shape.
Once the cookies from Step 4 are completely cool, spread or pipe the frosting from Step 5 onto each cookie. For a classic look, I like to use a small offset spatula to create a slight dome of frosting, but you can be as generous or minimal as you prefer. Serve immediately or store in an airtight container.