Preheat the oven to 350°F. Butterfly the 3 chicken breasts and carefully flatten them.
Place one slice of ham on top of each chicken breast. Season everything with salt and pepper. Place 2 slices of cheese on top of the ham on each chicken breast.
Roll up each chicken breast, place them next to one another, and stick 3 wooden skewers through them. Cut the chicken vertically between the skewers so you have 3 equally-sized shish kabobs. Generously brush the shish kabobs with olive oil and coat them in the bread crumbs.
Place the skewers on a baking tray and spread potato wedges all around them. Sprinkle rosemary over the potatoes and drizzle olive oil over everything. Transfer the pan to the oven and cook for 35 minutes.