Cut the pumpkin into bite-sized pieces and remove the seeds. Place in a bowl, cover with plastic wrap, and microwave at 600W for 5 minutes. Add salt, pepper, and mayonnaise, then mash until smooth or leave some texture as preferred.

Cut the sliced cheese into quarters.

Place cheese and mashed pumpkin mixture onto a slice of ham, then cover with another slice of ham to create a sandwich.

In a bowl, beat the egg and mix in the flour until smooth.

Dip the ham sandwiches into the batter, then coat with breadcrumbs.