Blend together the onion, garlic, and cumin with the water until smooth. Add the tomatoes a few at a time and blend until smooth. Heat the oil in a heavy pan, add the sauce, and fry until reduced and seasoned--about 8 minutes. Add the water or chicken broth with salt and cook for 5 more minutes. Keep warm while you prepare the fritters.
Put the whole guaje beans into a bowl, stir in the onion, cheese, and eggs--salt only if necessary, depending on the strength of the cheese. Heat the oil in a skillet--it should be about 1/2 inch deep--and fry large spoonfuls of the mixture over high heat until golden brown on both sides. Drain well.
Add the fritters to the warm sauce and cook over low heat, turning them over once, until the guajes are cooked inside--about 30 minutes.