Place ham, turkey, and mashed potatoes on a microwave-safe plate and cook in the microwave until heated through, about 2 minutes.
Lay out two slices of bread; place 4 slices of ham on each slice of bread.
Lay out remaining two slices of bread; place 1 slice of turkey on each slice of bread. Spread 1/2 the potatoes on top of each turkey slice. Place turkey slice of bread together with ham slice of bread to form sandwiches.