Heat oil in a large skillet over medium heat and cook the diced onion for 3-4 minutes until softened and translucent. Add the minced garlic and cook for just 30-45 seconds until fragrant, then remove from heat. Stir in the shredded chicken, drained green chiles, sour cream, 3/4 cup Monterey Jack cheese, 1/4 cup green enchilada sauce, and ground cumin until well combined. The filling should be creamy and cohesive. I like to taste it at this point and adjust the seasoning if needed—a pinch of salt can really brighten the flavors.
Preheat your oven to 375°F. While it heats, spread a thin, even layer of the 16 oz green enchilada sauce across the bottom of a 9x13 inch baking dish. This layer prevents sticking and ensures the enchiladas have sauce underneath for even cooking and flavor throughout.
Warm the tortillas briefly (either in a dry skillet for 10-15 seconds per side or by wrapping them in a damp paper towel and microwaving for 20-30 seconds) to make them pliable and easier to roll without cracking. Working with one tortilla at a time, place it on a clean surface and spoon about 1/3 cup of the chicken filling from Step 1 down the center. Roll it tightly and place it seam-side down in the prepared baking dish. Repeat with remaining tortillas, arranging them snugly in a single layer. I find that warming the tortillas really makes a difference—they don't tear and the enchiladas hold together beautifully.
Pour the remaining 16 oz green enchilada sauce evenly over all the rolled enchiladas, making sure to coat them thoroughly so they stay moist while baking. Top with the remaining 1.5 cups of shredded Monterey Jack cheese, spreading it evenly across the top for even melting and a golden finish.
Place the baking dish in the preheated 375°F oven and bake for 20 minutes, until the cheese is melted and bubbly and the sauce is bubbling around the edges. The enchiladas are done when you see the sauce beginning to bubble up the sides—this indicates they're heated through. Remove from the oven and let rest for 2-3 minutes before serving. Garnish with fresh chopped cilantro and serve warm.