Peel the potatoes, rinse, and slice into even as possible slices. Add the sliced potatoes to a pot for cooking. Slicing them as evenly as possible allows for cooking to be even throughout the potatoes.
Add enough water to the pot to cover the potatoes (to about 1/2" above the potatoes). Bring to a boil over high heat. Once the potatoes begin to boil, reduce the heat to medium high, and continue to boil for 15 minutes.

Drain the cooked potatoes in a colander. Drain them well! Watery potatoes don't make good mashed potatoes.

Add softened butter to a mixing bowl. Use a hand mixer to whip the potatoes a minute or two to get things started. Stop and scrape down the bowl to be sure all potato chunks are down in the area so you can get to everything with the mixer. Add salt, pepper, heavy cream, and mayonnaise. Continue to mix until smooth and creamy.

Transfer the mashed potatoes to a serving bowl. Serve hot.