Set an oven rack so that it's in the top third of the oven and preheat the broiler. Line a baking sheet with parchment paper or aluminum foil.
Wash and dry the poblano peppers and lay them out on the baking sheet so that they are not touching.
Set the peppers under the broiler until the skin is about 90% blackened on one side. Remove from the oven and, using tongs, turn the peppers over. Put them back under the broiler. Continue to turn the peppers until their skins are blackened on all sides.
Place the peppers in a bowl, cover with a dish towel and let them cool to room temperature.
In the meantime, add the oil and diced onion to a large high-sided skillet or sauce pan and set it over medium heat. Cook until the onion is soft and just beginning to turn golden. Add the cumin, paprika, garlic, ½ tsp salt, and ½ tsp ground black pepper. Cook, stirring constantly, for 1 minute longer.
Add all the remaining ingredients to the pan except for the rice, cilantro, and lime juice.
Set a lid on the sauce pan so that the pan is partially covered. Let simmer on low heat, stirring every once in a while, for about 20 minutes. After 20 minutes, the mixture should be thickened and condensed. If the mixture is on the runny side, remove the lid, turn the heat to medium high, and cook, stirring constantly, until the excess liquid has evaporated.
Remove from the heat and stir in the rice, cilantro, and lime juice. Taste and add more salt, pepper, and/or lime juice if you like. Set aside to cool slightly while you peel the peppers.
Preheat the oven to 350 degrees F (176 degrees C).
For each pepper, use a knife to slice the pepper open, lengthwise. Remove the stem and seeds and gently pull off and discard the blackened skin. Place the peppers in a 9 x 13 baking dish.
Open each pepper and add a generous amount of filling; wrap the pepper around the filling.
Bake the peppers uncovered for 20 minutes. Serve with extra enchilada sauce or Mexican adobo, and sour cream or vegan sour cream.
