For the Red Velvet Cookies:

1. Prepare Dry Ingredients: In a medium-sized bowl, whisk together the all-purpose flour, cocoa powder, baking soda, and salt. Set aside.
2. Cream Butter and Sugar: In a large mixing bowl, beat the softened butter and granulated sugar together with an electric mixer on medium speed for 2-3 minutes, until light and fluffy.
3. Add Egg and Flavorings: Mix in the egg, red food coloring, vanilla extract, and vinegar. Beat until fully incorporated, ensuring the mixture has an even red color.
4. Combine Wet and Dry Ingredients: Gradually add the dry ingredients into the wet ingredients, mixing on low speed until just combined. Be careful not to overmix to maintain a tender cookie texture.
5. Chill the Dough: Wrap the dough in plastic wrap and refrigerate for at least 30-45 minutes. Chilling the dough helps prevent the cookies from spreading too much during baking.
6. Preheat the Oven: While the dough chills, preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper.
7. Shape and Bake: Scoop 1-tablespoon-sized portions of dough and roll them into balls. Place them on the prepared baking sheets about 2 inches apart, and press down gently to flatten slightly. Bake for 10-12 minutes or until the edges are set but the centers remain soft.
8. Cool: Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.

For the Cream Cheese Filling:

1. Beat Butter and Cream Cheese: In a large mixing bowl, beat the softened butter and cream cheese together until smooth and creamy.
2. Add Sugar and Vanilla: Gradually add the powdered sugar, beating on low speed until combined. Mix in the vanilla extract and continue beating until light and fluffy, about 2-3 minutes.
3. Assemble the Cookies: Once the cookies are completely cooled, pipe or spread a generous amount of filling onto the flat side of one cookie. Top with another cookie to form a sandwich.