Heat oil in a 5-quart pot over medium heat. Cook onion and red pepper for 6 minutes, then stir in garlic and cumin for 30 seconds.
Mash 1 can of beans in a bowl with 1/2 cup of the measured broth until mostly smooth. Add the mash and remaining whole beans to the pot.
Pour in remaining broth and orange juice, then add salt and pepper. Bring to a simmer.
Simmer uncovered for 12 to 15 minutes, stirring from the bottom, until the soup thickens slightly and the pepper is tender.
Stir in lime juice off the heat. Divide among 6 bowls and add the yogurt evenly as small dollops.