Heat 3 TBSP oil in a medium skillet and add the diced potatoes. Cook over high heat for 5 minutes, stirring the entire time. Cover and cook over medium heat until fork tender, about 10 more minutes.
Meanwhile, heat the remaining 1 TBSP olive oil in a separate skillet over medium heat. Add the ham to the pan and cook (stirring occasionally) until the ham begins to crisp around the edges. This should take about 5 minutes, depending on how thick your ham is.
Once the ham is cooked, set aside and add the eggs, milk, and spinach to the pan. Stir well and cook over low heat until the eggs are no longer slimy - about 15 minutes. Break up the frozen spinach with a wooden spoon as you go.
Once all ingredients are cooked, spoon them into your tortillas, folding them into burritos as you go.
Refrigerate for use within 3 days or freeze for up to 3 months.