Pierce both potatoes a few times, put in the microwave and cook on high until cooked through, 5 to 10 minutes. Carefully remove the skin from the sweet potato. Dice both potatoes and set aside.
In a medium skillet, melt 2 tablespoons of the butter over medium heat. Add the bell peppers, squash, zucchini and onions and cook for a few minutes. Add the diced potatoes to the veggies and cook until golden brown. Season with salt and pepper.
In a separate pan, melt the remaining tablespoon of butter over medium heat and crack in the eggs. Cook until the whites have set, 3 to 4 minutes.
Serve up the hash with a fried egg on top of each portion.