** Fresh spinach: Wash well and remove and discard stems. Steam the spinach leaves about 5 minutes. Allow to drain in a colander or sieve, pressing very well to remove as much excess water as possible. Coarsely chop the spinach.
** Frozen spinach: Thaw the spinach. Put in a sieve and press very well to remove as much excess water as possible.
In a bowl, mix the pressed spinach with the chopped onion, garlic and cilantro. (see note) Using a fork, stir in the egg, salt and pepper. Stir in the corn tortilla meal or breadcrumbs, just enough so that the mixture holds together.
Divide the spinach mixture in 1/4 cup measures. In the palm of your hand, shape the mixture into small round patties, and as you do, poke 4 or 5 little pieces of the cheese in the middle. Forming them about 2 ½ inches wide, about 1/2 inch thick. (It may feel like the patties won’t hold together, especially if there is still a lot of moisture in the spinach. Handle them gently and they will cook nicely all in one piece.)
Over medium flame, heat a thin layer of the oil in a large skillet. Gently cook the patties, turning to cook both sides, about 3 minutes per side. Remove from the heat and keep warm while you prepare the sauce.