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Season the chicken with the ancho chile powder, salt and pepper. Heat a few tablespoons of oil in a medium high-sided ovenproof saute pan over high heat. Sear the chicken on both sides until golden brown. Add the chicken broth and barbecue sauce, bring to simmer, cover and cook in the oven until fork-tender, about 1 hour.
Remove the chicken from the pan, loosely cover and let rest for 15 minutes. Reduce the cooking liquid in the pan over medium-high heat until about 1/2 cup remains. Shred the chicken with a fork into bite-size pieces. Return the chicken to the pan and toss to coat in the mixture. Reserve.
For the chiles: Increase the oven to 375 degrees F. Toss the poblanos with the oil, salt and pepper. Place on a baking sheet and roast, turning occasionally, until blackened and soft, about 25 minutes. Transfer to a bowl and cover with plastic wrap to steam. Once cool enough to handle, scrape off the skins. Make a long slash in one side of each poblano, from stem to tip. Carefully remove and discard the seeds. Reserve.
For the tortillas: Line a baking sheet with paper towels. Heat the oil in a medium high-sided saute pan over medium heat until it begins to shimmer. Fry the 1/2-inch tortilla strips in batches, until just crisp, 20 to 30 seconds. Transfer with a slotted spoon to one side of the prepared baking sheet and season with salt. Fry the julienned tortillas and transfer with a slotted spoon to the other side of the baking sheet and season with salt. Reserve.
For the cooked tomato salsa: Combine the tomatoes, jalapeno, garlic and 1/2 cup water in a blender and blend until smooth. Heat the oil in a large saute pan over medium heat until it just begins to shimmer. Add the pureed tomato mixture, oregano, salt and pepper and cook until the mixture thickens slightly and becomes a deep red, about 15 minutes. Reserve.
For the migas-filled chile rellenos: Put the cream in a small saucepan over medium heat and cook until reduced by half; do not let it boil. Whisk in the cheese until melted; season with salt and pepper. Cover and keep warm over very low heat.
Melt the butter and oil in a large nonstick saute pan over medium heat. Add the onion and bell pepper and cook until soft, about 5 minutes. Add the jalapeno and cook for 1 minute. Add the eggs, season with salt and pepper and stir with a heat-proof rubber spatula until small curds form. Remove from the heat and fold in the pulled chicken, cilantro and 1/2-inch tortilla strips. Fill the roasted poblanos with the mixture.
To serve, spoon some of the cooked tomato salsa onto 8 large dinner plates, top each with a chile relleno and drizzle with some of the cheese sauce. Garnish with the julienned tortillas and cilantro leaves.