1. MAKE CRUMBS Adjust oven racks to lowest and middle positions and heat oven to 450 degrees. Pulse crackers and bread in food processor until coarsely ground. Drizzle in butter; pulse to incorporate. Bake crumbs on rimmed baking sheet on middle rack, stirring occasionally, until light brown, 3 to 5 minutes. Transfer to shallow dish. Leave oven on.
2. STUFF CHICKEN Following instructions to left, top each ham slice with 1/4 cup cheese and roll tightly; set aside. Pat chicken dry with paper towels and season with salt and pepper. cut pocket in thickest part of chicken, and stuff each breast with 2 ham-and-cheese rolls. Transfer chicken to plate, cover with plastic wrap, and refrigerate at least 20 minutes.
3. COAT AND BAKE Beat eggs and mustard in second shallow dish. Place flour in third shallow dish. One at a time, coat stuffed chicken lightly with flour, dip into egg mixture, and dredge in crumbs, pressing to adhere.
To Freeze: Freeze in freezer safe container.
To Reheat: Transfer chicken to clean baking sheet. Bake on lowest rack until bottom of chicken is golden brown, about 10 minutes, and then move baking sheet to middle rack and reduce oven temperature to 400 degrees. Bake until golden brown and chicken registers 160 degrees, 20 to 25 minutes. Transfer to cutting board, tent with foil, and let rest 5 minutes.