Divide the ground buffalo into 4 equal portions and shape each into a thin, flat patty; season both sides with salt and fresh pepper.
Heat a large skillet over medium-high heat and lightly spray with oil when hot.
Cook the patties 2 minutes per side or until cooked to your liking, then remove from the pan and set aside.
Wipe the pan clean, return to medium heat, and lightly spray with oil.
Place 4 tortillas in the pan (or cook one at a time if the pan is small). On each tortilla, sprinkle 2 tablespoons of shredded cheese, then 2 tablespoons of pico de gallo.
Top the pico de gallo with a cooked buffalo patty, then add another 2 tablespoons of pico de gallo and 2 tablespoons of cheese over the patty.
Place another tortilla on top, press gently, then flip and cook until the cheese is melted and the tortillas are golden on both sides.
Remove from the pan, slice into wedges if desired, and serve immediately.