Pound breasts between plastic wrap to an even 1/4-inch thickness; season with salt and pepper.

Add one ham slice and one cheese baton to each; roll tightly and secure seams with toothpicks.

Chill 20 minutes; coat in flour, beaten eggs with water, then panko.

Heat oil in an oven-safe skillet; brown over medium-high 2 minutes per side.

Bake at 375°F for 18 to 22 minutes until chicken reaches 165°F. Rest 5 minutes; remove every toothpick before slicing.