Preheat oven to 350˚F (180˚C). Line a muffin pan with cupcake liners.
In the bowl of a stand mixer fitted with a paddle attachment or a large bowl, beat together the butter and sugar until light and fluffy. Beat in the melted white chocolate, followed by the eggs one at a time, then the vanilla extract.
In a medium bowl, combine the flour, baking powder, baking soda, and salt.
Mix 1/3rd of the flour mixture into the butter until just incorporated, followed by half of the milk, 1/3rd of the flour, the remaining milk, and the remaining flour.
Transfer the mixture to the prepared muffin tins, filling them 2/3 full (I used an ice cream scoop). Bake in preheated oven just until cooked through and a toothpick inserted in the center comes out clean, 20-22 minutes. Allow to cool on wire racks.