Rinse and scrub potatoes, then pat dry. Using a microwave-safe bowl or plate, heat in microwave on high for 7-9 minutes until the potatoes are cooked through. Poke with fork or chopstick to test. Remove the bowl and set aside.
Meanwhile chop and slice carrots, red onion, ham and set aside.
Using another microwave-safe plate or bowl, microwave onion and carrots for 2 to 3 minutes until carrots are cooked. Remove the plate and set aside. Once cooled, use a paper towel to squeeze excess water from the onion.
In a large bowl, mix potatoes, carrots, onion, cucumber, ham, and mayonnaise. Use a firm spatula or serving fork to break potatoes. Season with salt and pepper to taste and serve cool or at room temperature.