On a stove over open gas flame, place 1 Poblano chile and roast until charred on all sides, turning with tongs. Repeat for all Poblanos. Place charred chiles in a plastic bag and let them steam for 3 minutes. Peel the chiles under running water by rubbing the skin off with your fingers. Make a small slit on the side and remove the stem, seeds, and veins. Slice into thick pieces, setting about 3 Poblanos aside for the Mexican sauce.
In a small bowl, mix the garlic powder, kosher salt, and 1 tablespoon canola oil. Rub the chicken breasts with the mixture. Place the chicken breasts on a cutting board. Top with Poblano slices and two Oaxaca cheese pieces placed crosswise. Roll up the chicken breast to enclose the Poblano and cheese. Secure with toothpicks.
Heat 2 tablespoons oil in a 12-inch non-stick skillet over medium high heat. Place the chicken and cook for 4 to 6 minutes, turning them once. Cover and cook for an additional 4 to 6 minutes, or until internal temperature reads 160 degrees and chicken is no longer pink in the center. Remove the toothpicks. Cover with foil and set aside.
In a blender, add the 3 Poblano chiles, sour cream, chicken broth, onion, cilantro, garlic, and chicken bouillon granules. Blend until the sauce is smooth.
Place the sauce in a 2-quart non-stick sauce pan over medium heat, stirring constantly with a wire whisk, for 5 to 6 minutes, or until heated through. Cut the chicken breasts into slices and place on a platter. Top with the sauce.