3 cups sifted cake flour (not self-rising; sift before measuring)
2 teaspoons baking powder
1 teaspoons baking soda
1/2 teaspoon salt
2 sticks unsalted butter, softened
2 cups granulated sugar
2 teaspoons pure vanilla extract
3 large eggs, warmed in shell in warm water 10 minutes
2 cups well-stirred plain whole-milk yogurt (not Greek-style) atroom temperature 30 minutes
2 cups fresh red currants (1/2 pound), stemmed
4 cups fresh raspberries (16 ounces), divided
2/3 cup granulated sugar room temperature 30 minutes
3 cups confectioners sugar
3 tablespoons light corn syrup
1/2 cup heavy cream
Scant 1/2 teaspoon pure vanilla extract
Equipment: a 13- by 9-inch cake pan