Bring a medium pot of salted water to a boil. Add the tomatillos, jalapenos, and onion wedges; cover and simmer until tender, about 10 minutes. Drain well and transfer to a blender along with 1/3 cup of the cilantro. Puree until just slightly chunky and season to taste with salt.

Meanwhile, heat 1 Tbs. of the oil in a large skillet over medium-high heat. Add the beef, chopped onion, cumin, 1 tsp. salt, and 1/4 tsp. pepper and cook, stirring occasionally to break up the meat, until cooked through, about 5 minutes. Stir 1/2 cup of the salsa verde into the beef.

Position a rack about 6 inches from the broiler and heat the broiler to high. Grease a 9x13-inch metal or ceramic baking dish with the remaining 1/2 Tbs. oil.

Wrap the tortillas in a few slightly damp paper towels and microwave on high until warm, 30 to 45 seconds. Working with one tortilla at a time, spoon some of the beef mixture down the center of the tortilla and sprinkle with 1 Tbs. of the cheese. Roll up snugly and transfer to the prepared baking dish, seam side down. Repeat with the remaining tortillas and beef mixture. Pour the remaining salsa verde over the enchiladas and sprinkle with the remaining cheese. Broil until golden brown and bubbly, 3 to 5 minutes. Garnish with the remaining cilantro and serve.