Preheat broiler with oven rack 6 inches from heat. Coat a rimmed baking sheet with cooking spray. Place tomatillos, poblanos, onion, and garlic on prepared baking sheet. Broil for 12 minutes, turning vegetables after 6 minutes, until well charred. Let stand 5 minutes. Scrape mixture and any accumulated juices into a blender. Add cilantro leaves and stems, cumin, and 1/2 teaspoon each salt and black pepper; process until smooth.
Heat oil in a Dutch oven over medium-high. Sprinkle chicken with remaining 1/2 teaspoon each salt and black pepper. Place chicken in a single layer in Dutch oven, meaty sides down. Cook until browned, 5 to 6 minutes. Transfer to a plate.
Pour tomatillo mixture into Dutch oven. Bring to a boil over medium-high. Cook until sauce thickens slightly, 3 to 5 minutes. Return chicken to Dutch oven; reduce heat to medium-low; simmer until a thermometer inserted in thickest portion registers 165°F, 12 to 15 minutes. Place chicken on a plate; let stand 5 minutes. Set aside 2 cups tomatillo mixture. Shred chicken and return to Dutch oven; discard bones. Toss meat to coat.
Preheat oven to 350°F. Coat 2 (11- x 7-inch) baking dishes with cooking spray. Spread 1/4 cup reserved tomatillo mixture in the bottom of each dish. Spoon 1/4 cup chicken mixture into each tortilla; fold into thirds, and arrange in dishes (8 enchiladas in each). Spread 3/4 cup reserved tomatillo mixture over enchiladas in each dish. Sprinkle each with 3/4 cup cheese. Coat 2 pieces of aluminum foil with cooking spray, and cover each dish. Follow freezing directions, or continue to step 5.
Bake at 350°F for 15 minutes, until heated through. Remove foil. Increase heat to broil. Broil for 1 to 2 minutes, until cheese is golden and bubbly. Top each serving with 1 tablespoon yogurt and 1 tablespoon chopped cilantro.
How-To FREEZE: Cover dish with heavy-duty aluminum foil or an airtight lid. Freeze up to 2 months. THAW: Remove foil; reserve. Place dish in microwave. Microwave on MEDIUM for 20 minutes, until thawed. REHEAT: Cover dish with reserved foil. Bake at 350°F for 30 minutes, until cheese is melted and a thermometer inserted in center registers 160°F. Remove foil during last 5 minutes.