Preheat a heavy grill pan. Sprinkle the chicken generously with salt and pepper.
In a heavy saute pan, heat the vegetable oil over medium heat. Add the onions and garlic and cook until translucent, about 4 minutes. Remove from the heat.
In a mixing bowl, beat the egg. Add the breadcrumbs, oregano and thyme. Add the chicken to the bowl and top with the cooked onions and garlic. Mix well until all of the ingredients are evenly incorporated. Use a 1/2-cup scoop to measure out the patties and form 6 even ovals.
Grill the patties until fully cooked, about 5 minutes per side. Serve on a warmed bun smeared with some Pasilla Aioli. Top each burger with a slice of cheese, a lettuce leaf, tomato slice and some Poblano Rings.
Put the pasilla chile and garlic in a food processor and process until the garlic is minced. Add the mayo and process for about 2 minutes. Season the aioli with salt and pepper.
Preheat the broiler or a grill pan over high heat. Broil or grill the poblanos until the skins are charred. Transfer to a covered bowl until cool enough to handle, 10 minutes. Remove the skins and seeds, and then slice into 1/4-inch-wide rings.
Heat the oil in a large heavy saucepan or a deep fryer until a deep-fry thermometer inserted in the oil reaches 350 degrees F.
Meanwhile, arrange 3 mixing bowls in an assembly line. Mix together the flour and 1 teaspoon salt in the first. In the second, place the eggs and beat them. Fill the third with the breadcrumbs and ground guajillo and mix together.
Carefully drench the poblano rings in the flour, making sure not to break them. Shake off any excess flour and then soak in the egg wash. Then cover with the panko mixture. Fry until crisp and golden in color, about 2 minutes. Transfer to a paper towel to remove excess oil, and then season heavily with salt.