Peel and dice potatoes. They should be able an inch thick.
Place in a large pot and cover with 2 inches of water.
Bring to a boil over high heat.
Boil for 10-15 minutes, or until tender. You should be able to stick a fork in them and have it break in two pieces. They're not quite cooked if the fork comes out cleanly. And they're overdone if it breaks apart completely, instead of just in half.
Drain and place back in the pot.
Add the Greek yogurt, butter, salt, and pepper.
Mash with a potato masher until light and fluffy. Making sure to scrape the sides and stir occasionally.
Bake Mashed Potatoes
Preheat oven to 350 degrees Fahrenheit.
Lightly grease a baking dish.
Add mashed potatoes and cover with eggs and cheese.
Bake for 15 minutes, or until the cheese begins to brown.