Blend 2 cans of the beans with the tomato paste and 1 cup of vegetable broth until the beans are broken down into a thick (but not necessarily smooth) paste.
Heat a large pot over medium-high heat. Add the bean paste, remaining black beans, and remaining broth, and stir to combine. Add the cumin, oregano, salt, and pepper and let simmer for about 15 minutes, until fully warmed through and slightly reduced.
Ladle into 4 bowls and top each serving with 1 tablespoon of plain Greek yogurt.