Using an electric mixer, cream the butter and sugar together until extremely light and fluffy, 3-5 minutes. Then add the vanilla, vinegar and egg and beat until well combined.
Then beat in the salt, cocoa powder and food coloring, scrape the bowl and beat again for even coloring. Add the flour slowly and beat until just combined. Press the dough flat on a piece of plastic wrap, and wrap well. Refrigerate for at least one hour.
Preheat the oven to 375 degrees F and line two cookie sheets with parchment paper. Flour a work surface, then roll the dough evenly to 1/8-inch thick. Using a 2-inch heart cookie cutter, cut out the cookies close together. Use a small spatula to carefully move them to the cookie sheets. Gather the remaining dough and reroll and cut to get 32-34 cookies. (Cut the cookies close together and do not roll the dough more than twice, or the cookies will be tough.)
Bake for 6-8 minutes. They should come out of the oven soft, not crisp. Cool completely on the baking sheets.
Using an electric mixer, beat the cream cheese, vanilla, and salt together. Slowly add the powdered sugar until smooth. Place the frosting in a piping bag.
Turn half of the cookies over and pipe a thick ribbon of frosting in a V shape on the flipped cookies. Press a lollipop stick into the frosting, then gently press another cookie on top to flatten out the frosting. Allow the red velvet cookie pops to dry a bit (30 minutes) for the frosting to set up and hold the cookie on the stick. Sprinkle with powdered sugar and serve.