Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a bowl, whisk together the flour, baking powder, baking soda, salt, and cocoa powder. Set aside.
In a large mixing bowl, cream the softened butter and granulated sugar together until light and fluffy.
Beat in the egg and vanilla extract until well combined.
Gradually add the dry ingredients to the butter mixture, alternating with the buttermilk, starting and ending with the dry ingredients. Mix until just combined.
Divide the batter into two bowls. Add red food coloring to one bowl and blue food coloring to the other, mixing until you achieve your desired shades.
Using a tablespoon, drop spoonfuls of the red batter onto one baking sheet and the blue batter onto the other, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the tops spring back when lightly touched. Let cool on the baking sheets for 5 minutes before transferring to wire racks to cool completely.
For the filling, beat the softened butter in a mixing bowl until creamy. Gradually add powdered sugar and vanilla extract, mixing until smooth. Add milk, one tablespoon at a time, until the filling reaches your desired consistency.
Once the cookies are completely cool, spread a generous amount of filling on the flat side of one cookie and sandwich it with another cookie. Repeat with the remaining cookies.