Remove the beef from the refrigerator and let it come to room temperature for at least 10 minutes. This technique lets the beef cook more evenly and faster.
Lightly coat a large, nonstick skillet with cooking spray and place over medium-high heat. Dry the beef with a paper towel and season each side with salt and black pepper. Add the filets to the skillet and cook until they are browned on one side, about 2 minutes. Flip them and brown on the opposite sides, about another 2 minutes. Transfer the filets to a wire rack set over a plate and set aside.
Reduce the heat to medium. Add the garlic to the skillet and cook until it is golden brown. Add the onions, red pepper flakes and kale, and sauté, stirring constantly, until the kale has started to wilt, about 1 minute. Add the water and cover the skillet. Bring to a simmer and cook until almost all the water has evaporated, about 4 minutes.
Remove the lid from the skillet. Add the tomatoes, olives and beans, and cook until the kale is tender and the sauce coats the leaves, about 1 minute.
Add the reserved filets to the skillet with all of the collected juice and cook to the desired doneness (1 to 2 minutes for medium-rare).
Remove the beef and place 1 piece on each of four plates. Add the cheese to the kale, and season with salt, if needed. Spoon the kale next to each filet of beef on the plates.