Set broiler to high.

Trim woody base from garlic cloves, then lightly smash with the side of a knife. Leave papery skin intact. Arrange garlic, tomatillos, onion, and peppers on a rimmed baking sheet. Set under the broiler. Check every few minutes. Use tongs to set any tomatillos that have burst in a bowl, turn the peppers, and grab any garlic that's starting to blacken. Continue until all the vegetables have roasted nicely, 10 - 15 minutes total.

Set pan aside to cool. Under cold running water, remove the skin, stems, and seeds from the peppers.

Place all of the roasted vegetables in the pitcher of a blender (you may need to do this in two batches), add 2 cups chicken stock, and pulse until mixture is well blended, but still has a bit of texture. (Use caution if mixture is hot.)

Pour into a sturdy pot and set over medium-low heat. Add 2 cups remaining chicken stock, stir, and then add sea salt to taste. Pull chicken meat from reserved roasted drumsticks, set in a small dish, and warm in the oven.

Meanwhile, set out a deep-frying pan and pour in neutral oil to 1-inch depth. Set over medium/medium-high heat. Fry tortilla strips until golden and crisp, about 3 minutes. Set cooked strips on a stack of paper towels and sprinkle with sea salt. (You can also skip the frying and use high-quality tortilla chips instead—but be mindful that store-bought chips can be very salty.)

Ladle soup into bowls, garnish with tortilla strips (or chips), chicken, avocado slices, a drizzle of crema, cilantro, and cotija. Serve soup with a lime wedge.