In a food processor, whirl black beans just until slightly chunky. Scrape into a bowl and stir in egg yolks, flour, baking powder, green onions, chilies, cumin, vinegar, and salt.
In another bowl, with a mixer on high speed, beat egg whites until they form soft peaks. Fold whites into black bean mixture just until incorporated. Gently stir in queso fresco.
Pour 1 teaspoon oil into a 10- to 12-inch nonstick frying pan over medium-high heat; when hot, drop batter in 1/4-cup portions into pan and spread into 2-inch-wide cakes with the bottom of measuring cup. Cook, turning once with a wide spatula, until cakes are browned on both sides and firm to touch in the center, about 6 minutes total. As cakes are cooked, arrange in a single layer on 12- by 15-inch baking sheets in a 200° oven; cover loosely with foil and keep warm up to 30 minutes. Repeat to cook remaining cakes, adding more oil to pan as necessary.