1) Make the sauce (or warm the jarred)
Homemade: Heat oven to 450°F. On a sheet pan, add tomatillos, onion, jalapeños, and garlic (still in the peel). Roast until tomatillos blister and soften, 12 to 15 minutes. Peel garlic. Blend roasted vegetables with broth, cilantro, cumin, oregano, and 1 tsp salt until smooth.
In a saucepan, heat oil over medium. Pour in sauce carefully (it may splatter) and simmer 8 to 10 minutes to mellow and thicken slightly. Stir in lime juice. Taste and adjust salt.
Jarred: Warm salsa verde with broth in a saucepan over medium-low until steamy and pourable. Simmer 3 to 5 minutes if it seems thin. Add lime juice if you want it brighter. Taste and salt if needed.
Sauce note: You should have roughly 4 cups sauce total, which is plenty for the pan (some goes under, some for dipping, the rest on top).

2) Make the filling
Lower oven to 400°F. In a large skillet, heat oil over medium. Add chopped onion and cook until soft, 4 to 5 minutes. Add garlic, cumin, and smoked paprika and cook 30 seconds.
Add shredded chicken and green chiles. Stir to coat, then turn off heat. Let cool for 2 minutes, then stir in sour cream and 1 cup Monterey Jack plus 1/2 cup cheddar. Taste and add a pinch of salt if it needs it.

3) Warm tortillas and assemble
Spread about 1 cup sauce in the bottom of a 9x13-inch baking dish.
Warm tortillas so they bend without cracking. My easiest method: wrap a stack in a damp paper towel and microwave 30 to 45 seconds.
Dip each tortilla quickly in warm sauce (just enough to coat), add a generous 1/3 cup filling (closer to 1/2 cup if you are only using 10 tortillas), roll, and place seam-side down in the dish. Repeat until snug. Use 10 tortillas if you fill them generously, or 12 for slightly smaller rolls that fit more easily in the pan.

4) Sauce, cheese, bake
Pour remaining sauce over the enchiladas. Top with remaining Monterey Jack and cheddar.
Bake uncovered until bubbly and lightly browned, 18 to 22 minutes. Rest 10 minutes before serving so everything sets up.
Finish with cilantro, scallions, or diced onion. If you like a creamy contrast, add a little extra sour cream on top.

5) Serve
Scoop generously. Make sure each plate gets a crispy edge piece. That is the law.