In a small saucepan over medium heat, add 2 teaspoons of vegetable oil. When hot, add the onion and cook for 4-5 minutes until the onion is just translucent. Add the poblano and jalapeño peppers, and the garlic, and cook for two minutes longer. Add the black beans, 1/4 cup of the turkey jus, the chili powder and the salt and pepper, and continue to cook, stirring occasionally for another 3 minutes. Using a fork, smash some of the beans against the side of the pan and stir to mix well. Remove the beans from the heat once they are completely heated through.
Heat the remaining 1 cup of turkey jus in a medium sauce pan over medium-low heat. Once the jus is hot, add the turkey and gently simmer for 2 minutes or just until the turkey is warm.
To assemble the quesadillas, lay 4 tortillas on a clean work surface and spoon 1/3 cup of beans on the bottom half of each tortilla. To each, add 1/2 cup of the turkey, 1/2 cup of the shredded cheese and then fold the quesadilla in half.
Heat a large sauté pan over medium-high heat, add 1 tablespoon of the canola oil and when hot add one quesadilla to the pan. Cook for 2 minutes on one side or until golden brown. Flip the quesadilla over and cook for another 2 minutes, or until the cheese has melted and the tortillas are golden brown. Remove the quesadilla from the pan to a baking sheet. Add the remaining oil to the pan and continue to cook the 3 remaining quesadillas in the same manner. If necessary, place the cooked quesadillas in a warm oven until ready to serve.
Cut each quesadilla into 4 pieces and serve immediately with the salsa, sour cream and cilantro if desired.