Preheat the broiler to high. Char the poblanos under the broiler on all sides, 5 to 6 minutes. Place in a bowl, cover and let cool. Peel, seed and slice.
Meanwhile, place the corn flour and corn kernels in a bowl and season with salt. Add the cheese and toss with your fingers. In a small saucepan, heat the milk but do not boil. Add the butter to melt. Stir into the corn mixture and let stand for about 10 minutes.
Place a bowl of warm water near the corn bowl and cover a baking sheet with parchment. With your fingers moistened from the water bowl, form the corn mixture into 3-inch mounds. Pat the mounds into 1/2-inch-thick cakes, making 10 to 12 arepas.
Heat a thin layer of oil in a large nonstick skillet over medium-high heat. Add enough cakes to fill the pan. Cook them for 3 to 4 minutes on 1 side, then flip and cook the second side for 1 to 2 minutes. Transfer to a plate. Repeat with the remaining arepas.
Add the bacon to the skillet and brown. Add the eggs; season with salt and the cilantro. Scramble to the desired doneness. Layer the eggs on the arepas and top with the poblanos.