HEAT grill to medium heat.
BLEND first 3 ingredients in blender just until blended. (Some chunks can remain.)
COMBINE oil, oregano and cumin; brush onto cactus. Grill 8 min. or until tender, turning occasionally. Transfer to plate.
SPREAD cactus with beans; top each with 1 Tbsp. tomatillo mixture. Cover with onions and cheese. Serve with remaining tomatillo mixture.