Using a large mixing bowl, mix the flour, cocoa powder, baking powder, and salt. Stir until blended thoroughly.
In a large bowl, use an electric mixer to beat the butter and sugar until light and fluffy. Beat in the eggs, vanilla extract, and red food coloring until smooth and completely mixed together.
Use the mixer, on low speed, to add the flour and cocoa mixture to the batter until well blended. Cover the the bowl of cookie batter with plastic wrap and chill for 2 to 4 hours, until very firm.
Preheat the oven to 350 F. Then, line a large baking sheet with parchment paper or spray with nonstick baking spray.
Use a fine-mesh strainer to sift the powdered sugar into a mixing bowl.
Using your hands, roll the dough into small cookie balls, about 1-inch in diameter. Place each ball of dough on the cookie sheet, about 1.5 inches apart. When all of the balls are formed, roll each one into the sifted powdered sugar and return it to its place on the baking sheet. Leave the remaining dough in the refrigerator, to keep chilled, between batches.
Bake the cookies for 10 to 12 minutes, until they have a crinkled appearance. Allow the finished cookies to cool for 4 or 5 minutes before transferring to a cooling rack. Repeat the procedure with the remaining dough.
Adjust the amount of food coloring a little at a time to get the color that you want. Liquid food coloring is less concentrated than the gel and paste type. So, you may need more or less, depending on what form you are using.
Use a small scoop to measure dough, to keep the cookies uniform in size. Then shape with your hands.
Be sure to keep the cookie dough in the refrigerator, between batches.