Prep Tempeh: Using a box grater, roughly grate the tempeh.
Flavor Base: Heat oil in a large pot over medium heat. Add onion and garlic, cooking until onion is slightly soft and translucent, about 5 minutes.
Cook Tempeh: Add the grated tempeh, cumin, coriander, oregano, pepper, and salt. Cook until tempeh is lightly browned, about 5 minutes.
Beans: Scooch tempeh mixture to one side of the pot. Add the beans to the empty side of the pot. Using a potato masher or fork, roughly mash about 1/3 of the beans.
Soupify: Add broth and sauerkraut. Bring to a simmer for 5 minutes. Right before serving, mix in cilantro and lime juice.
Serve: Serve hot, topped with grated white cheddar cheese and a dollop of Greek yogurt.
Notes
*Can sub one or both of the cans of cannellini for navy beans.