Place the Poblano Peppers on a foil lined backing sheet and place under the Broiler (on high) for 5 minutes than flip them over and roast another 5 minutes
Place the roasted Poblanos in a zip lock bag to allow them to cool
Heat the Oil in a large sauce pan or Dutch oven over Medium heat. Add the Onions and cook for 2 minutes until softened then add the Garlic and Cilantro and cook for 3 more minutes
Stir in the Flour to coat the Onions, Garlic and Cilantro then stir in the Chicken Stock, Heavy Cream, Milk, Salt and Pepper. Bring to a simmer.
Remove the Poblanos from the bag. Cut off the tops and run them under warm water to help remove the skin and to remove the seeds
Dice up four of the Poblanos and place them in the Soup along with the Pepper Jack Cheese. Simmer for another 20 minutes
Chile Relleno Topping
Cut the fifth Poblano in half.
Whisk the Eggs yolks in their bowl and whisk the Whites in their bowl for 2 minutes. Add the flour and pepper to the bowl with the Egg Whites and whisk some more to combine
Heat the Oil in a small skillet over medium heat
Dip the Poblano halves first in the Egg yolks then in the Egg White Mixture then place in the hot oil. Fry each side 1-2 minutes until golden brown. Drain on a paper towel and cut each half in half
Ladle the Soup in a bowl and top with one of the Poblano quarters. Serve with tortilla Chips, cut up Tomato, sliced Avocado and a lime wedge