Stir together beef consommé, French onion soup, and water in a saucepan. Bring to a simmer over medium heat.
Add roast beef; cook until heated through, about 2 minutes. Using tongs, transfer roast beef to a plate, letting any excess liquid drip back into saucepan. Reserve jus in saucepan.
Place bread slices on a work surface. Use a rolling pin to flatten each slice on both sides until smooth and evenly thin.
Place 1 provolone cheese slice and about 2 slices (about 1 1/4 oz.) of roast beef over each bread slice. Roll bread tightly from short side, pressing seams gently to adhere. Place roll-ups seam side down. Brush each roll-up on all sides with melted butter.
Lightly coat an air fryer basket with cooking spray. Arrange 6 rolls seam-side down in air fryer basket in a single layer. Cook at 400 degrees F (200 degrees C) until toasted, golden, and crisp, about 5 minutes. Repeat with remaining 6 rolls.
Divide hot jus among 4 small bowls. Serve rolls with jus for dipping.
