Position a rack in the center of the oven and preheat to 400 degrees . In a saucepan, simmer the broccoli rabe in water until crisp-tender, about 5 minutes. Drain, then coarsely chop.
Lay a chicken breast, smooth side down, on a work surface. Place 1 ham slice lengthwise over half of the breast. Top with 1/4 cup broccoli rabe and 1 cheese slice. Fold the breast in half lengthwise to cover the filling; secure with toothpicks. Repeat with the remaining chicken, ham and cheese.
Place the cornflakes in a dish. In a bowl, whisk the egg whites and paprika. Coat each breast with the egg mixture, then the cornflakes; transfer to a foil-lined baking sheet. Bake until cooked through, about 30 minutes. Let rest for 5 minutes.
Meanwhile, in a saucepan, whisk the sour cream, mustard and 1/4 cup water over medium heat for 1 to 2 minutes.
Discard the toothpicks. Slice each breast crosswise and drizzle with the sauce.