Make the red velvet cake. In a bowl, whisk together the flour, sugar, cocoa powder, and baking powder. Add the milk, apple cider vinegar, melted butter, and red food coloring. Stir just until combined. The batter should be thick and smooth.
Cook the cake. Transfer the batter to a large microwave safe mug or small oven safe dish. Microwave for 70 seconds to 1 minute, until the cake rises and sets. Or bake in a preheated 350°F oven for 15–20 minutes. Check doneness with a toothpick. It should come out clean. Let the cake cool completely.
Prepare the buttercream. Beat the butter using a hand whisk or electric whisk in a bowl until light and fluffy. Add the powdered sugar and mix until smooth. Beat in the milk and vanilla until creamy.
Form the cake pop mixture. Crumble the cooled cake into a mixing bowl. Add 2 tablespoons of the buttercream and mix until the texture is moist and holds together when pressed.
Shape the cake pops. Scoop small portions and roll into smooth balls. Place on a plate or tray.
Insert the sticks. Dip the tip of each wooden stick into melted white chocolate, then insert it halfway into a cake ball. Refrigerate for 10 minutes to set.
Dip and decorate. Dip each cake pop into the melted white chocolate, letting excess drip off. Immediately add sprinkles, then stand upright in a Styrofoam block or similar holder.
Set and serve. Refrigerate the cake pops for about 15 minutes, until the coating is firm. Serve once set.