Place cornmeal in a mixing bowl and season with a little salt. Add cheese and jalapeno or pepper. Toss with fingertips to combine.
In a saucepot, heat milk but do not boil. Melt in butter then stir into cornmeal and cheese mixture. Let stand about 15 minutes to cool.
Place a bowl of warm water near a mixing bowl and cover a baking sheet with parchment. With moistened fingers, form 3-inch balls of the cornmeal mixture. Pat each ball into corn cakes about half an inch thick. (Make 4 large balls for entre size or 8 small balls for appetizer size)
Place a bowl of warm water near a mixing bowl and cover a baking sheet with parchment. With moistened fingers, form 3-inch balls of the cornmeal mixture. Pat each ball into corn cakes about half an inch thick. (Make 4 large balls for entre size or 8 small balls for appetizer size)
Heat a thin layer of oil in a large, non-stick skillet over medium to medium-high heat. Add enough cakes to fill pan and cook 5 minutes on first side, flip and cook to golden on the second side, 2-3 minutes more. Repeat with remaining batter.
Once all the arepas are done, add chorizo to pan and brown. Add scallions and toss to combine. In a bowl, beat the eggs with some salt and the cilantro or parsley, and add to the pan. Scramble to desired doneness. Gently split the corn cakes and fill with eggs.