Preheat oven to 400*F. Line a baking sheet with parchment paper, drizzle olive oil on the parchment. Prepare the poblanos at the same time you roast the jalapenos and place in the same container to sweat the skins. Skin and deseed the poblanos. Chop the poblanos into 1/2 inch pieces. Set aside.
Chop the white onion into 1/2" pieces and set aside.
Filet open the chicken and pound out to an even thickness, between 1/2 and 3/4". Toss into a bowl with the olive oil, onions, garlic cloves and spices. Toss to coat evenly.
Place chicken, onions, and garlic cloves on the parchment lined baking sheet and place in the oven. Bake for 10 minutes.
After 10 minutes add the chopped poblano pieces. (I found that adding them at the beginning chars them because they are already mostly cooked from roasting them.) Bake for another 10 - 12 minutes. (Total baking time 20-22 minutes, adjust as necessary.)
Remove everything from the oven. Remove the garlic and smash it, then add to a bowl with the veggies. Shred the chicken and then add to the bowl of veggies, add the juiced lime and stir well.