In a large bowl, mix together masa and salt. Add water, a little bit at a time, until a soft, pliable, nonsticky dough is formed.
Using damp hands, form dough into 2 1/2-inch balls. Flatten each ball into a 4-inch patty and place 1/4 cup cheese in the center of each. Fold sides of patties over cheese to enclose and reshape into a ball. Flatten each ball into another 4-inch patty.
Preheat a griddle and lightly coat with oil. Place patties on skillet and cook, turning once, until golden brown, about 4 minutes per side. Serve immediately with curtido and salsa.
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