Heat oven to 425°F. Toss sweet potato and poblano with oil, cumin, and 1/4 teaspoon salt on sheet pan. Roast 25 to 30 minutes, turning once, until tender and browned.
Reduce oven to 350°F; butter a 9-by-13-inch dish. Whisk eggs, milk, and remaining salt; pour into dish. Bake 14 to 18 minutes until just set and center 160°F. Cut into short strips.
Spread vegetables and egg strips in shallow containers; refrigerate within 2 hours and chill fully before assembly. Refrigerate beans and cheese too.
Divide vegetables, eggs, beans, and cheese evenly among tortillas. Fold sides in; roll tightly. Wrap separately; bag and freeze up to 2 months for best quality.
Unwrap one frozen burrito completely; loosely wrap in damp paper towel. Microwave on microwave-safe plate at 50 percent power 3 minutes; turn and heat at full power in 1-minute intervals to 165°F in center, usually 2 to 4 minutes more.
Rest 1 minute. For firmer tortilla, toast in dry skillet over medium 1 to 2 minutes per side. Recheck middle if any part feels cool.