How to Make It
Preheat the oven to 325°. Line a 12-cup muffin pan with paper liners. In a medium bowl, whisk the flour with the baking powder and salt. In a small bowl, whisk the milk with the vanilla.
In a stand mixer fitted with the paddle, beat the butter with the sugar at medium-high speed, scraping down the bowl once or twice, until light and fluffy, about 2 minutes. At medium-low speed, beat in the eggs one at a time until incorporated. At low speed, beat in the dry ingredients and the milk mixture in 3 alternating additions until smooth. Spoon about 1/4 cup of the batter into each prepared cup.
Bake the cupcakes for 25 to 30 minutes, until a toothpick inserted in the centers comes out clean. Let cool in the pan for 5 minutes, then cool completely on a wire rack, about 1 hour.
Working with 1 cupcake at a time, peel off the liner. Turn the cupcake top side down in the palm of one hand, cover with the other hand and gently twist off the cake top. Reserve the cupcake bottom for another use. Arrange the top smooth side down on a platter. Repeat with the remaining cupcakes. Freeze the tops for 1 hour.
Spread 1/4 cup of the ice cream onto each of 6 cupcake tops. Close the sandwiches with the remaining cupcake tops and gently press together. Freeze for 30 minutes before serving.