In a large skillet, melt butter over medium heat.

Layer half of the thinly sliced potatoes, chopped onion, chopped green pepper, and diced ham in the skillet.

Repeat the layers, seasoning each layer with salt and pepper.

Cover the skillet and cook for 10 to 15 minutes, or until the potatoes are tender.

Pour the lightly beaten eggs over the potato mixture, cover, and cook for an additional 3 to 5 minutes until the eggs are almost set.

Sprinkle shredded Cheddar cheese over the entire skillet.

Remove from heat, cover, and let it stand until the cheese is melted.