Preheat the oven to 375°F and grease a 9-by-13-inch or 3-quart baking dish.
Bring a medium pot of water to a boil. Add the kale leaves and simmer, stirring once or twice, until just wilted, about 30 seconds. Drain, pat dry, and coarsely chop. Squeeze any excess water out of the kale.
In a large bowl, whisk the eggs with the milk, chopped cilantro, jalapeño, garlic, and ½ cup of the cheese. Season lightly with salt and pepper.
Layer the tortilla chips in the prepared baking dish with the corn, black beans, and kale. Pour the egg mixture over the top, making sure everything is evenly distributed. Dollop the tomatillo salsa over the top. Bake the strata until it is just set around the edges, but still a little wobbly in the middle, about 20 minutes.
Scatter the remaining ½ cup of cheese over the top. Bake until the middle of the casserole is just set and the cheese on top is melted, about 5 minutes more. Let cool for 5 minutes, then garnish with scallions, radish, cherry tomatoes, and avocado. Serve with salsa roja and Mexican crema.