Heat the birria per the box (about 5 minutes in the microwave, or until simmering on the stovetop). Lift the beef out and reserve the broth for dipping.
Shred any large pieces with two forks, then let the beef drain in a strainer for a few minutes so the filling isn't wet.
Toss the drained beef with the cilantro and diced onion.
Lay an egg roll wrapper in a diamond shape. Add a line of cheese and 2–3 tablespoons of beef across the center. Fold the bottom corner over the filling, fold in the sides, and roll tightly. Dab the final corner with water to seal.
Preheat the air fryer to 375°F (190°C). Lightly spray each egg roll all over with oil.
Arrange in a single layer, seam-side down, without crowding. Air fry 8–10 minutes, flipping halfway, until golden and crisp.
Serve hot with warm consommé for dipping.