Cut tenderloin in half lengthwise. Place each half between two sheets of plastic wrap and pound to 1/8-inch thickness.
Season pork with salt, pepper, and cayenne; spread a thin layer of mustard on top. Grate Monterey Jack cheese onto the pork. Sprinkle parsley on top. Fold in the pointiest end 1/3 of the way. Fold in the sides. Give pork another fold; fold remaining end on top. Flip cutlets seam-side down in the plastic wrap and lightly pound until flattened.
Unwrap cutlets and season again with salt, pepper, and cayenne. Dust on all sides with flour until lightly coated. Place beaten egg and bread crumbs in two shallow dishes. Dredge each cutlet in egg, then cover with bread crumbs. Let cutlets rest for 10 to 15 minutes.
Heat at least 1/4 inch oil in a pan over medium heat. Cook each cutlet until crust is browned and until meat springs back when poked, 4 to 5 minutes per side.