2 (4-ounce) cans diced green chiles, drained, or 12 fresh Hatch chiles, diced
14 large eggs
1/3 cup milk
½ teaspoon salt
2 tablespoons unsalted butter
½ cup minced fresh cilantro
8 (10-inch) flour tortillas
2 cups shredded cheddar cheese
2 cups shredded jalapeño cheese
Directions
To make the pickled vegetables, in a large bowl, combine the onion, carrots, jalapeño, and cauliflower.
In a medium saucepan, combine the water, vinegar, sugar, salt, garlic, and oregano. Bring the mixture to a boil over high heat, then pour it over the vegetables in the bowl. Set aside until cooled to room temperature, then refrigerate until ready to serve.
To make the burritos, bring a medium saucepan of salted water to a boil over high heat. Add the potatoes and cook for about 10 minutes, until tender but not too soft. Drain and set aside to cool.
Heat the oil in a large nonstick skillet over medium-high heat. Add the onion, bell pepper, and potatoes and cook, stirring occasionally, until the potatoes start to turn golden. Stir in the ham and half of the green chiles and cook for 1 minute. Remove the pan from the heat.
In a large bowl, whisk together the eggs, milk, and salt until well mixed. Heat the butter in a large nonstick skillet over medium heat. (You may have to cook the eggs in two batches, depending on the size of your pan.) Add the eggs and cook, stirring constantly, until mostly set. Before the eggs are thoroughly cooked, stir in the remaining green chiles and the cilantro. Let the eggs cool.
Tear 8 large squares of aluminum foil. In a large, dry skillet, heat the tortillas one by one until they are pliable and easy to fold. Place each warmed tortilla on a square of foil. Top each tortilla with an equal amount of the cheeses, potato mixture, and egg mixture. Roll up the tortilla like an egg roll, then roll the burrito in the foil the same way. (The wrapped burritos can be frozen for future use. To reheat from frozen, remove the foil and rewrap the burrito in a paper towel. Heat in the microwave for 1–2 minutes, until warm throughout. Or leave the foil wrap on and reheat the burrito in the oven at 350 degrees F for 15 minutes.)
To serve, slice the burritos on the diagonal and serve with to-go cups of pickled vegetables.