In a large pot, add the cow's feet and enough water to cover them. Bring to a boil, then reduce heat and let simmer for 30 minutes.
Drain the water and rinse the cow's feet. Add fresh water to the pot, enough to cover the cow's feet again. Add the onion and garlic and bring to a boil.
Reduce heat and let simmer for 1 hour, or until the cow's feet are tender.
Add the carrots, celery, and potatoes to the pot and enough water to cover the vegetables. Bring to a boil, then reduce heat and let simmer for 20 minutes.
Add the diced tomatoes, tomato paste, thyme, and cumin to the pot. Season with salt and pepper, to taste. Add more water, if needed.
Let the soup simmer for an additional 10 minutes, or until all the vegetables are tender and the flavors have melded together.