Halve large tomatillos (more than 2 inches in diameter) and place them skin-side up for broiling in step 2 to ensure even cooking and charring.
You can substitute three 11-ounce cans of tomatillos, drained and rinsed, for the fresh ones in this recipe if necessary.
If you can’t find poblanos, substitute 4 large jalapeño chiles (with seeds and ribs removed). To increase the spiciness of the sauce, reserve some of the chiles’ ribs and seeds and add them to the food processor in step 4.
For fresh salsa, chopped fresh tomatoes, chopped sweet onion, chopped ancho/poblano/pasilla/jalapeno/serrano chilies (your preference or a combination of several), chopped fresh cilantro, dash of garlic powder, chili powder, ground cumin, seasoned salt, and a squeeze of fresh lime juice. Mix and adjust seasonings to your taste.
2Adjust oven racks to middle and highest positions and heat broiler. Heat 2 teaspoons oil in medium saucepan over medium heat until shimmering; add onion and cook, stirring frequently, until golden, 6 to 8 minutes. Add 2 teaspoons garlic and cumin; cook, stirring frequently, until fragrant, about 30 seconds. Decrease heat to low and stir in broth. Add chicken, cover, and simmer until instant-read thermometer inserted into thickest part of chicken registers 160 degrees, 15 to 20 minutes, flipping chicken halfway through cooking. Transfer chicken to large bowl; place in refrigerator to cool, about 20 minutes. Remove 1/4 to 1/2 cup liquid from saucepan and set aside; discard remaining liquid.
3Meanwhile, toss tomatillos and poblanos with remaining 2 teaspoons oil; arrange on rimmed baking sheet lined with foil, with poblanos skin-side up. Broil until vegetables blacken and start to soften, 5 to 10 minutes, rotating pan halfway through cooking. Cool 10 minutes, then remove skin from poblanos (leave tomatillo skins intact). Transfer tomatillos and chiles to food processor. Decrease oven temperature to 350 degrees. Discard foil from baking sheet and set baking sheet aside for warming tortillas.
4Add 1 teaspoon sugar, 1 teaspoon salt, remaining teaspoon garlic, and half the reserved cooking liquid to food processor; process until sauce is somewhat chunky, about eight 1-second pulses. Taste sauce; season with salt and pepper and adjust tartness by stirring in remaining sugar, 1/2 teaspoon at a time. Add more of the reserved liquid if desired. Set sauce aside (you should have about 3 cups).
5When chicken is cool, pull into shreds using hands or 2 forks, then chop into small bite-sized pieces. Combine chicken with cilantro and 1 1/2 cups cheese; season with salt.
6Place tortillas on 2 baking sheets. Spray both sides of tortillas lightly with cooking spray. Bake until tortillas are soft and pliable, 2 to 4 minutes. Remove tortilla pans and increase oven temperature to 450 degrees (Alternate method: spray 6 tortillas at a time on each side with cooking spray and stack on a small microwaveable plate, cover with damp paper towel and microwave for 30-60 seconds until soft and pliable, repeat as the tortillas are used so they stay pliable enough to roll easily.)
7Smear bottom of 13- by 9-inch baking dish with 3/4 cup tomatillo sauce. Place warm tortillas on cutting board or countertop and spread approx 1/3 cup filling down center of each tortilla. Roll each tortilla tightly and place in baking dish, seam-side down.
8Pour remaining tomatillo sauce over top of enchiladas. Use back of spoon to spread sauce so that it coats top of each tortilla. Sprinkle with remaining 1/2 cup cheese and cover baking dish with foil.
9Bake enchiladas on middle rack until heated through and cheese is melted, 15 to 20 minutes. Uncover, sprinkle with scallions, and serve immediately, passing radishes,sour cream and fresh salsa separately.