Set a rack in the center position and preheat the oven to 450 degrees. Spray 4 6-ounce ramekins with nonstick cooking spray.
Melt the butter and white chocolate in the top of a double boiler, stirring until smooth. When completely melted, stir in the confectioners' sugar.
Lightly whisk the eggs and egg yolks in a large bowl. Stir in the red food coloring and melted chocolate mixture.
Whisk the cocoa and flour in a small bowl to combine. Add to the batter and stir until just combined.
Divide the batter evenly among the ramekins. Place the ramekins on a baking sheet and bake until the sides of the cake are set but the centers are still soft , 14 to 15 minutes. Let the cakes rest for 2 minutes, then invert them onto dessert plates.
Serve the cakes immediately, dusted with confectioners's sugar and with berries on the side.