Preheat oven to 350°. Line 12 muffin cups with paper liners. Place yogurt and 3/4 cup corn in a food processor; process until blended.
In a large bowl, beat butter and sugars until blended. Beat in egg. In another bowl, whisk together flour, baking powder, baking soda and salt. Add to butter mixture alternately with yogurt mixture, beating after each addition. Fold in remaining 1/2 cup corn.
Fill prepared cups half full. Bake until a toothpick inserted in center comes out clean, 15-18 minutes. Cool 10 minutes before removing from pan to a wire rack; cool completely.
For frosting, in a small heavy saucepan, melt butter over medium heat. Heat until golden brown, 5-7 minutes, stirring constantly. Transfer to a large bowl; cool slightly. Beat in remaining ingredients until smooth. Spread over cupcakes. Store cupcakes in a covered container.
Decorative cupcake liners can be found at fancyflours.com.