Place a cheese slice between two bologna slices and press edges together.
Set up three bowls: flour, beaten eggs, and breadcrumbs.
Dredge each sandwich in flour, then egg, then breadcrumbs.
Heat about 1/2 inch of oil in a skillet over medium heat.
Fry the melts 2–3 minutes per side until deep golden and crisp.
Drain on paper towels for 1 minute.
Toss cooked macaroni with mayonnaise, peas, carrots, and diced ham.
Serve the hot melts immediately with a scoop of macaroni salad.
Tip: Keep the cheese centered and smaller than the bologna to prevent leaking.