In a medium bowl, mash your beans with a fork until mostly smooth.
Add ½ the pepper jack cheese, ¼ cup of the panko, garlic, salt, cumin, and oregano to the bowl. Use the fork to mix well. Portion the mixture into 4 and form each into a ½-inch patty, packing well to keep together. Place the patties on a plate.
Stir together the remaining ¾ cup of panko with the garlic powder on another plate.
In a small bowl, lightly whisk together the egg with the water.
Using a pastry brush, coat the top of one patty thinly with the egg mixture. Place the patty egg-side down on the panko-garlic mixture. While the patty is still on the panko mixture, brush the plain side of the patty with egg wash and carefully flip the patty to coat with panko. Gently place the patty back on the plate and repeat with the remaining patties.
Heat a nonstick pan over med-high heat. Spray with nonstick cooking spray. Put the patties and fry for 3 minutes. Spray the tops lightly with cooking spray and carefully flip the patties. Sprinkle the tops with the remaining pepper jack cheese. Cook for 2 minutes, then cover the pan with a lid or cover with a large metal bowl if using a griddle pan. Cook for another 2 minutes or until the cheese is melted.
Serve on buns with your favourite burger toppings.