In a large microwave-safe bowl, toss potatoes with 2 tablespoon oil and 1/4 teaspoon salt. Microwave uncovered, until potatoes soften but still hold shape, about 10 minutes, gently stirring every couple minutes. Drain potatoes.
Heat 1 tablespoon oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add potatoes in a single layer and cook until golden brown on first side, 5 to 7 minutes. Gently stir potatoes to rearrange, and cook until tender and golden brown on second side, 5 to 7 minutes. Transfer from skillet to a large bowl and set aside.
In a medium bowl, whisk together the eggs, milk, salt, and pepper. In the now empty skillet over medium heat, add the egg mixture and cook, stirring often, until soft and scrambled. Transfer eggs from skillet to the large bowl.
Use the same skillet over medium heat to cook the sausage, peppers, and onion, stirring often, until sausage is cooked through. Drain grease, if needed.
Add the potatoes and eggs back to the skillet with the sausage and stir to combine. Add the cheese and stir until melted. Salt and pepper to taste.
Spoon the mixture onto the tortillas and roll each up burrito-style. Serve immediately, if desired. You can wrap each burrito in plastic wrap and keep refrigerated for a few days, or store in a resealable freezer bag in the freezer to reheat at a later date.
Campfire option: Wrap each in heavy duty foil and keep refrigerated or cold. Then cook the wrapped burritos in the hot coals of a campfire, until heated through, about 8-10 minutes depending on your fire. Turn once during cooking. Try to keep them out of the flames and just in the hot coals, or the outside of the burrito will cook too fast and the inside will still be cold.