Preheat your oven to 375 degrees.
In a large bowl add the kidney beans and mash with a fork or a potato masher. Next, fold in the curry powder, eggs, parsley, Parmesan, kosher salt, and black pepper.
Fold in the panko breadcrumbs. If you need to add more panko to the bean mixture that's okay. The panko is meant to soak up any moisture. Once everything is combine, take the bean mixture and form 4 patties. Let the patties rest for about 10 minutes before cooking.
Next, in an oven-safe, non-stick skillet add the olive oil. Preheat the skillet medium-high heat and then add the bean patties. Brown on both sides for about 3 minutes per side. Transfer the skillet to the oven to cook through about 10 to 12 minutes. In the last minute of cooking add the sliced cheddar cheese ton top of each bean patty.
To serve: place a bean patty on top of the bottom burger bun. Garnish with a tomato slice, arugula, and mayonnaise. Enjoy.