Adjust the oven racks to the upper-middle and lower-middle positions and heat the oven to 350°F. Toss the tortillas with two tablespoons of oil in a large bowl, then spread them across two rimmed baking sheets. Bake until the tortillas are brown and dry, 16 to 24 minutes, flipping them halfway through. Let them cool, then increase the oven temperature to 500°F.

Heat the remaining tablespoon of oil in a 12-inch skillet over medium-high heat until it shimmers. Add the poblanos, half of the onions, and the salt; cook until the vegetables are softened and lightly browned, 6 to 8 minutes.

Stir in two tablespoons of the cilantro, the garlic, and the chipotle, and cook until fragrant. Add the water and tomatoes with their juice, then simmer until the flavors have melded and the sauce is slightly thickened, 10 to 15 minutes.

Transfer the sauce to a blender and process until smooth, about 1 minute—be careful when blending hot liquids. Return the sauce to the now-empty skillet, season with salt and pepper to taste, and bring to a simmer over medium heat.

Add the beans and cook until warmed through, about 5 minutes. Use a potato masher to coarsely mash the beans directly in the pan until they are somewhat broken down but still have texture.

Stir in the baked tortillas and cook until they just begin to soften, about 2 minutes.

Transfer the mixture to an 8-inch square baking dish and sprinkle with the cheese. Bake on the lower-middle rack until the casserole is hot throughout and the cheese is melted, 5 to 10 minutes.

Whisk the sour cream and lime juice together. Let the casserole cool slightly, then drizzle the sour cream mixture over the top. Sprinkle with the chopped tomato, the remaining onions, and the remaining cilantro and serve warm.