Over medium heat, rest the hatch chiles on the grate of a gas stove, rotating the chiles every 30 seconds or so, and until the outsides are charred and skins are blistered. Dice the chiles, discarding the seeds, and set aside. Repeat this process with the corn, rotating the ears of corn every 30 seconds or so. Cut the kernels off the cob. Transfer the diced chiles and corn kernels to a bowl, along with the red onion, cumin, garlic powder, 4 ounces of crumbled queso fresco and a squeeze of lime. Mix and toss until combined.
To soften the tortillas, microwave them for 10 seconds or so. Alternatively you can place tortillas between two damp paper towels, put them on a baking sheet and transfer them to a 200-degree F oven for 5-10 minutes. (This is the method I like to use.)
Preheat oven to 350 degrees F. In a 9 x 12-inch casserole dish, add 3/4 cup enchilada sauce (measurement can be eyeballed). Spoon a few tablespoons of corn mixture onto the center of each tortilla. Fold over filling, placing the enchilada seam side down in the casserole dish. Repeat the process with the remaining tortillas and mixture. Top with the remaining 1 cup enchilada sauce and sprinkle on the cheese.
Bake for 15 minutes until cheese melts. Garnish the enchiladas with lime, cilantro and a handful of the remaining queso fresco. Serve immediately.