Trim any excess fat from the chicken breasts. If they are particularly thick, gently pound them to a more even thickness so they cook more consistently. Pat them dry and season lightly with salt, pepper, garlic powder, onion powder, and paprika.
In a medium bowl, whisk together the condensed cream of chicken soup, milk, and Dijon mustard until smooth. This mixture creates a creamy sauce that complements the ham and Swiss cheese.
Place the raw chicken breasts in a single layer in the slow cooker. Avoid stacking them too deeply, as this can cause uneven cooking.
Place one slice of ham over each chicken breast. Fold the ham as needed so it fits neatly over the chicken. The ham adds savory flavor and gives the dish its classic cordon bleu character.
Pour the prepared soup mixture evenly over the chicken and ham. Use a spoon to distribute the sauce around the chicken so the ingredients are coated.
Cover the slow cooker and cook for approximately 3–4 hours on LOW or 2–3 hours on HIGH, depending on the slow cooker and the thickness of the chicken. Check the chicken's internal temperature with a food thermometer; it must reach 165°F (74°C) in the thickest part.
Once the chicken is cooked through, place a slice of Swiss cheese over each breast. Cover the slow cooker for another 5–10 minutes, or until the cheese melts.
For a crunchy finish, combine the breadcrumbs with melted butter and Parmesan cheese. Toast the mixture in a skillet or bake it separately until golden brown. Sprinkle over the chicken just before serving.
Sprinkle chopped fresh parsley over the finished dish. Spoon the creamy sauce over each chicken breast and serve hot with mashed potatoes, rice, egg noodles, or steamed vegetables.