Drain all cans of beans and rinse. Place 1 can's worth of black beans and 1 can's worth of kidney beans in the food processor. With a slotted spoon, add about ½ of the can of diced tomatoes. Add the chilies. Pulse until a paste forms.
Heat a heavy-bottomed stock pot over medium heat. Add about 2 tablespoons of olive oil. Add the onion and garlic, and saute for a few minutes, until translucent. Add the cumin, cayenne, and paprika. Continue cooking until fragrant and slightly toasted, 5 minutes.
Add the paste and remaining beans and tomatoes to the pot. Add the stock and bring to a boil, stirring well. Once boiling, bring down to a simmer and cook for about 20 minutes, stirring occasionally.
Serve over a bed of rice. Top with desired toppings and enjoy warm. Seal in an airtight container in the refrigerator and simply reheat to enjoy later.