Preheat the oven to 450 °F.
On a baking sheet, drizzle the chicken breasts with olive oil, season with salt and pepper, and sprinkle with the garlic powder and dried oregano. I like to quarter the onion that will go in the sauce and add it to the pan, along with the garlic cloves and jalapeño, to roast with the chicken.
Bake the chicken about 17 minutes, until fully cooked.
While the chicken bakes, char the poblanos on a hot grill or over a gas stove, until blackened on all sides. Place the charred poblanos in a plastic bag or airtight container to steam for 10 minutes.
After the steam has loosened the charred skin, use a paper towel and your hands to remove the charred skin from the poblanos. At this point, you can also remove the seeds and stems, slicing the peppers open so they lay flat.
For the sauce, add the tomato puree, salt, dried oregano, black pepper, bay leaf, and cinnamon to a sauce pan and bring to a simmer.
When the chicken is done, add the onion, garlic cloves, and jalapeño (stem removed and seeded, if desired) to the sauce. Allow to simmer until slightly thickened, about 20 minutes. This will be thicker than traditional chile rellenos sauce, because we don’t want to add too much extra moisture to the casserole. Remove the bay leaf and puree the sauce, either with an immersion blender or in batches using a traditional blender.
Shred the chicken breasts and quarter the tortillas.
Prepare to assemble the casserole: Start with a thin layer of sauce in the bottom of your casserole dish, then layer on shredded chicken, the shredded cheeses, peppers, and tortillas.
Continue with another layer of sauce, layering the ingredients until you run out or the dish is filled to the top. Reserve about 1 cup shredded cheese to finish over the top layer of the casserole.
Bake the casserole, covered, at 400 °F for 15 minutes, then uncovered for another 10 minutes until the top is golden and bubbly.
Serve, with lime for squeezing if desired!