Make the cupcakes: Preheat the oven to 350 degrees F. Line a 6-cup jumbo muffin pan with paper liners. Whisk the flour, baking powder and salt in a bowl.
Beat the butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Beat in the eggs, one at a time, then beat in the vanilla. Reduce the mixer speed to low; beat in the flour mixture in 3 batches, alternating with the strawberry milk, beginning and ending with flour, until just combined.
Divide the batter evenly among the prepared muffin cups. Bake until a toothpick comes out clean, 25 to 30 minutes. Let cool 5 minutes in the pan, then remove to a rack to cool completely.
Using a paring knife, cut a cone-shaped piece of cake out of the top of each cupcake (about the same size as the strawberries), stopping about 1/2 inch from the bottom. Stuff with the strawberries, then cover with a small piece of the removed cake.
Make the frosting: Sift the confectioners' sugar and cocoa powder into a medium bowl. Transfer half of the sugar-cocoa mixture to a large bowl; add the butter and 1/4 cup cream and beat with a mixer on medium-high speed until smooth. Add the remaining sugar-cocoa mixture and 1/4 cup cream and beat until fluffy. Transfer to a pastry bag fitted with a star tip and pipe onto the cupcakes. Top each with a strawberry half.