Heat 2 teaspoons oil in a 12-inch nonstick skillet over moderately high heat until hot but not smoking, then saute chorizo and onion, stirring, until onion is softened. Add potatoes with salt and pepper to taste and cook, covered, stirring occasionally, until potatoes begin to turn golden brown, about 6 minutes. Stir in jalapenos, tomatoes, and cumin and cook, uncovered, stirring occasionally, until potatoes are tender and golden brown, about 6 minutes.
Transfer to a bowl and cool completely. Stir in cilantro, cheese, and salt and pepper to taste.
Roll out each empanada wrapper into a 6-inch round on a lightly floured surface. Put about 1/3 cup filling in center of each wrapper and form filling into a log. Moisten wrapper edges with a finger dipped in water and fold each wrapper over filling to form a half-moon. Press down around filling to force out air and seal by pressing edges together firmly with a fork.
Heat remaining 3 cups oil in a deep 12-inch skillet over moderate heat until hot but not smoking, then fry empanadas in 3 batches, gently turning, until golden brown, about 3 minutes. Transfer empanadas to paper towels to drain.
Empanadas may be filled 1 day ahead and chilled in 1 layer on a lightly floured plate, covered. Reseal edges if necessary.