Begin by preheating your oven to 350°F (177°C). Line a mini muffin pan with 24 cupcake liners, ensuring they fit snugly.
In a large mixing bowl, combine the cake flour, baking powder, and salt. Whisk thoroughly to distribute the dry ingredients evenly.
In a separate bowl, mix together the melted butter and oil until they form a silky consistency. Gradually incorporate the granulated sugar while mixing on low speed until the mixture turns light and airy.
Add the room-temperature egg and vanilla extract, whisking until the mixture becomes smooth and cohesive.
Alternate between the dry ingredients, milk, and sour cream while mixing into the wet ingredients: start with one-third of the dry mixture, followed by half the milk, then another third of the dry mix, the sour cream, and finish with the remaining dry mix. Mix gently until just combined, being cautious not to overwork the batter.
Using a tablespoon-sized cookie scoop, fill each mini cupcake liner with batter, ensuring an even distribution.
Bake in the preheated oven for 10–14 minutes, or until the edges turn lightly golden and the tops spring back when gently pressed.
Allow the cupcakes to cool in the pan for 10–15 minutes. Then transfer them to a wire rack to cool completely before applying the frosting.