Set your oven to 350°F (175°C). Line a baking sheet with parchment paper.

In a large mixing bowl, beat softened butter and granulated sugar until light and fluffy, about 2 minutes. Add the egg and vanilla extract and mix until combined.

In another bowl, whisk together all-purpose flour, baking soda, baking powder, and salt. Gradually incorporate this mixture into the wet ingredients on low speed to form a thick but soft dough. Add the milk and mix until just combined.

Divide the dough into five portions. Tint each portion with a different gel food coloring, kneading until the color is evenly distributed.

Roll tablespoon-sized dough portions into smooth balls and place them 2 inches apart on the prepared baking sheet. Bake for 8-10 minutes until the edges are set and the tops show slight cracks. Let cool on the baking sheet for 5 minutes, then transfer to wire racks to cool completely.

Beat softened butter in a bowl until smooth. Gradually add powdered sugar, then mix in heavy cream (or milk), vanilla extract, and a pinch of salt until fluffy and spreadable.

Pair cooled cookies of similar size. Spread a generous amount of filling on the flat side of one cookie, then top with another cookie. Press gently to evenly spread the filling.

Allow the assembled cookie sandwiches to rest for about 10 minutes so the filling firms and melds the cookies together.