Heat broiler to high. Place the tomatillos, poblanos, onion, and garlic cloves on a large baking sheet. Broil for 8-10 minutes, turning 2-3 times, until the peppers and tomatillos are well charred on all sides. Remove from oven and place the peppers in a bag or covered bowl to sweat for 10 minutes, then peel and remove the seeds. Remove the garlic cloves from the wrappers.
Add the tomatillos, poblanos, onion, garlic, 1/2 cup cilantro, lime juice, and a heavy pinch of salt and pepper to a food processor or blender. Whip until smooth. Taste and adjust seasonings as desired. This should make about 1 1/2 cups of salsa verde.
Preheat oven to 400 degrees. Grease a 9 x 13 inch casserole dish, or a large oven-safe skillet.
Bring a large pot of water to a boil. Cook the shells according to package directions. Drain.
In a large bowl, combine the ricotta, the remaining 1/2 cup of cilantro, and 1 cup of monterey jack cheese.
Pour 1/2 of the salsa verde on the bottom of the dish or skillet. Scoop about 1 tablespoon of the ricotta filling into each shell and nestle into the dish/skillet until all the filling and shells are used. Pour the remaining salsa verde overtop and sprinkle the remaining jack cheese and cheddar overtop.
Bake the shells for 15-20 minutes until the cheese melts and bubbles. If desired, switch the broiler on for the last 2-3 minutes to brown the tops. Watch closely.
Serve warm garnished with extra cilantro, lime, and crumbled cotija/feta, as desired.