Preheat the oven to 350°F. Line 24 cupcake tins with baking papers. Place the butter in a medium, heatproof bowl placed over a pot of gently simmering water. When the butter is just melted, whisk in the brown sugar. Let cool to lukewarm temperature, about 4 minutes.

Whisk the eggs into the mixture. Add the milk, vanilla, baking powder, and salt; whisk to combine. Whisk in the flour until evenly combined.

Fill each baking paper two-thirds full. Bake until a skewer inserted into the middle of a cupcake comes out clean, about 20 minutes.