Pour the potatoes in in a single layer. Let them brown and then flip them over to brown the other side.
While the potatoes cook, beat the eggs in a bowl.
Add salt and pepper to taste.
Stir in the cheese.
When the potatoes are done, add in the ham and pour the eggs over the top.
Let the eggs cook, stirring only enough to help them cook.
Warm tortillas and fill with the egg mixture.
Notes
If not serving immediately, wrap in foil sprayed with nonstick spray. They can be reheated in the oven, or unwrapped and microwaved. To store in the freezer, place foil-wrapped burritos in a large ziplock bag and thaw in the refrigerator overnight.