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Preheat oven to 325F. Line muffin pans with 18 cupcake liners.
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In a medium bowl, whisk together flour, baking powder and salt. Set aside.
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In a small, microwave-safe bowl, melt the chopped white chocolate by heating it in 30 second intervals in the microwave. Stir well with a fork between each interval and cook only until the chocolate is smooth when stirred.
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In a large bowl, cream together butter and sugar until light. Beat in eggs one at a time, followed by melted white chocolate and vanilla extract. Working in two or three additions, alternate adding in some of the milk and some of the flour mixture, ending with a final addition of flour. Mix until just incorporated and no streaks of flour remain.
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Divide batter evenly into prepared muffin cups. Bake at 325F for 20-23 minutes until a tester comes out clean and the tops spring back when lightly pressed with a fingertip. Cool completely before frosting.