In a dry skillet over medium heat, toast the chile pieces until fragrant, 1–2 minutes. Set aside.

Heat a large (6–8 quart) saucepan over medium heat. Add the onion and garlic and cook, stirring often, until beginning to brown, 4–6 minutes, adding a splash of water as needed to prevent sticking. Transfer to a blender along with the toasted chiles, tomatoes, and smoked paprika. Puree until smooth.

Return the pot to medium heat. Add the puree and cook, stirring nearly constantly, until thickened to the consistency of tomato paste, about 6 minutes. Add the broth, water, oregano, and pinto beans. Bring to a boil, then reduce to a simmer. Cook for 30 minutes.

While the soup simmers, heat the oven to 375°F. Cut each tortilla in half, then slice into 1/4-inch strips. Spread in a single layer on a baking sheet, sprinkle lightly with salt, and bake about 15 minutes, stirring every 5 minutes, until golden and crisp. Let cool.

Add the greens to the soup and cook until wilted—about 2 minutes for spinach, longer for chard or kale. Season to taste.

Ladle into bowls and top with tortilla strips and avocado. Serve with lime wedges.