Heat the oil in a large soup pot over medium-high heat with a bit of the onion. When the onion begins to sizzle, add the rest of the onion, jalapeños, poblanos, Anaheim peppers, and garlic. Sauté for about 5 minutes, stirring often.
Add the escarole, salt, peppers, paprika, cumin, and oregano. Cook, while stirring, for about 2 minutes.
Stir in the broth and beans. Bring to a simmer and cook for about 15 minutes.
Garnish each bowl with a dollop of yogurt.