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HEAT oil in large skillet on medium-high heat. Add onions, chiles and garlic; cook 2 min., stirring frequently. Stir in mushrooms; cook 15 min. or until all liquid is released, stirring occasionally. Stir in ham. Keep warm.
MEANWHILE, mix masa harina, salt and water until mixture forms soft dough. Divide into 10 pieces; flatten each to 5-inch disk. Heat large skillet on medium-high heat; cook sopes, in batches, 2 min. or until lightly browned on both sides, turning every 30 sec. Use your thumb and forefinger to make 1/4-inch-high rim around edges of sopes.
FILL with mushroom mixture; top with cheese.