Preheat the broiler to 550 degrees F. Line a baking sheet with parchment paper and set aside.
Peel onion and cut several slices to create a dozen or so rings of red onion; set aside for serving. Roughly chop the remaining onion and transfer to the parchment paper along with the tomatillos.
Broil until the vegetables are soft and slightly brown, 7 to 10 minutes, turning as needed. Transfer the vegetables and any liquid to a blender, add the broth, salt, sugar, and half the cilantro; puree until smooth. Spoon about ¼ cup of the salsa into the bottom of a 9 x 13-inch baking dish and spread to cover the surface; set aside.
Meanwhile, stack the tortillas, wrap in a damp paper towel and microwave just until warm and soft, 1 minute; keep covered. Toss the chicken with 1½ cups shredded cheese in a bowl. Spoon a portion of the chicken mixture down the middle of each tortilla. Roll and place the enchiladas seam side down in the prepred baking dish. Repeat with remaining tortillas and chicken mixture. Brush tops of the tortillas with olive oil. Broil until crisp and golden, 3-4 minutes.
Pour the tomatillo sauce over the enchiladas and top with the remaining ½ cup shredded cheese. Return to the oven and broil until the cheese is bubbly and golden brown, 3 to 5 minutes. Garnish with the onion rings, queso fresco, and remaining cilantro.