In a 12-inch skillet heat 2 tablespoons of the oil. Dip each tortilla, one at a time, into the oil just until hot. Drain on paper towels (do not stack), reserving oil in skillet. Keep 4 of the tortillas warm on a baking sheet in a 300 degrees F oven. Reserve remaining tortilla.
Meanwhile, for salsa, in the oil remaining in the skillet cook onion and garlic for 2 to 3 minutes or until tender. Stir in drained tomatoes, chile peppers, cilantro, and cumin. Bring to boiling; reduce heat. Simmer, uncovered, for 5 minutes. Transfer mixture to a blender or food processor. Tear reserved tortilla into pieces and add to blender or food processor. Cover and blend or process until a coarse puree. Keep warm.
In the skillet heat remaining 1 tablespoon oil over medium heat. Carefully break eggs into skillet. When whites are set, add water. Cover skillet and cook eggs to desired doneness (3 to 4 minutes for soft-set yolks or 4 to 5 minutes for firm-set yolks).
Place a warm tortilla on each of four dinner plates. Top each with 2 fried eggs. Spoon some of the warm salsa over the eggs. Sprinkle with cheese. If desired, garnish with cilantro sprigs. Makes 4 servings.