Line a small colander with 3 layers of 100% cotton cheesecloth or a clean paper coffee filter. Suspend colander over a bowl and spoon in yogurt. Cover with plastic wrap and chill overnight to create yogurt cheese.
Remove yogurt cheese from strainer; discard liquid. Transfer to a large bowl. Stir in garlic, cumin, and salt. Fold in sweet pepper, corn, black beans, tomato, green chilies, 1 1/2 cups mexican cheese and 3 tablespoons cilantro.
Spoon into crock or spread on a platter. Top with remaining mexican cheese and cilantro.