Set your oven to high broil with a rack set in the top ⅓ of the oven
While the oven is heating, arrange your peppers on a sheet pan with a rack. Place rack under the broiler to blister and char the skins of the peppers. 7-8 minutes/side. Once blistered and charred on both sides, remove from oven and set aside to cool.
Heat a large skillet over medium heat with 1 tablespoon of olive oil. Once hot add the onion and garlic and cook until the onion is translucent. Add the sweet potatoes, cumin, chili powder, and salt and cook until the sweet potatoes are fork tender. About 10 minutes.
Deglaze the bottom of the pan with ¼ water and the lime juice, scraping the bottom of the pan with the wooden spatula.
Add the shredded chicken and mix evenly with the sweet potato mixture, followed by the black beans. Stir in the black beans until just combined. Do not over mix the beans or the mixture could turn black.
Turn off the heat and allow mixture to cool while you prep your cooled poblano peppers
For each pepper, using a knife, make an incision long ways, from the stem of the pepper to the tip to make a pocket for the filling. Do not cut all the way through the pepper. If you don't like the skin, the skins will easily remove at this step. If you prefer milder food, use a spoon to scrape out the ribs and seeds of the peppers.
Using a spoon, add filling to each pepper. The peppers should be over stuffed. Be careful not to tear the peppers when filling. Depending on the size of your peppers, ¾ - 1 cup of filling will fill each pepper.
Return pan to a 350°F oven for 10-15 minutes until heated through. Serve with limes, crema, avocado, salso and/or cilantro.