Heat the oven to 425°F (220°C). Toss the potatoes with 1 tablespoon of oil, 1/2 teaspoon of salt and the paprika, spread on a sheet pan and roast for 25–30 minutes, stirring once, until crisp.
Whisk the eggs, milk and remaining salt. Heat the remaining oil in a large nonstick skillet over medium-low heat, add the spinach and stir until wilted, then pour in the eggs.
Cook, stirring gently, until the eggs are just set but still slightly moist, about 4–5 minutes. They will firm up when reheated.
Spread the potatoes, eggs and beans on a tray and let them cool completely, about 20 minutes.
Warm the tortillas briefly so they are pliable. Divide the eggs, potatoes, beans and cheese among them, placing the filling in a line in the lower third.
Fold in the sides, roll up tightly and wrap each burrito in foil or parchment. Freeze in a zip-top bag.
