Position the rack in the middle of the oven and crank the heat to 400°F (200°C). Brush two 12-well mini-muffin tins (1 3/4-by-7/8-inch) with butter. Set aside.
Heat the milk and butter in a small saucepan over low heat until the butter is melted. Remove the pan from the stove and let the mixture cool until warm.
In a large bowl, rub the lemon and orange zests into the sugar with your fingers until fragrant.
Dump in the flour, baking powder, and salt and whisk to combine.
Stir the egg, yolk, and vanilla into the warm milk mixture and then pour it into the flour mixture in several additions, stirring gently until the ingredients are just incorporated and the batter is smooth.
Spoon the batter into the prepared pans, three-quarters full. Bake until the cakes are well-risen and golden brown, 18 to 20 minutes.
Transfer the pans to a rack, cool for 5 minutes, and then pop out the mini cakes. Serve warm piled high in a napkin-lined basket or large cake stand.