In a medium bowl, whisk together 2¼ cups all-purpose flour, 2 cups granulated sugar, 2 tablespoons unsweetened cocoa powder, 2 teaspoons baking powder, and ½ teaspoon salt until evenly combined.
In a large bowl, use an electric hand mixer to beat 8 ounces room-temperature cream cheese and 4 tablespoons (½ stick) room-temperature unsalted butter on medium speed until smooth and no lumps remain, about 1–2 minutes. Scrape down the bowl as needed.
Add 1 large egg, 1 teaspoon vanilla extract, and 1 tablespoon red food coloring to the cream cheese mixture. Beat on medium speed until fully incorporated and the mixture is evenly colored, scraping the bowl once.
Add the dry ingredients to the creamed mixture and mix on low speed just until a uniform dough forms and no streaks of flour remain. Do not overmix.
Cover the dough tightly with plastic wrap and chill in the refrigerator for at least 2 hours, or until firm enough to scoop.
When ready to bake, preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper. Place ½ cup powdered sugar in a shallow bowl for rolling.
Use a 1-tablespoon measure to scoop portions of dough. Roll each portion quickly between your hands to form a ball (about 1 tablespoon of dough). Roll each ball in the powdered sugar to coat, then place on the prepared baking sheets at least 3 inches apart.
Bake in the preheated oven for 10–12 minutes, or until the edges of the cookies are set but the centers may still look slightly soft.
Remove the baking sheets from the oven and let the cookies cool on the sheets for a few minutes, then transfer the cookies to a wire rack to cool completely.
Store cooled cookies in an airtight container for up to 3 days.