Place soaked beans in a medium saucepan and cover with water. Bring to a boil over high heat, reduce heat to medium-low, and simmer until cooked through, about 1 1/2 hours, adding more water if needed. Drain beans into a colander set over a bowl and reserve the cooking liquid from the beans.
Heat oil in a medium saucepan on the grates of the grill. Add the onions and cook until soft. Add the rice, toss to coat in the oil and onion mixture, and cook for 2 minutes. Add 3 3/4 cups of the bean cooking liquid (if there is not enough liquid, add some water to measure 3 3/4 cups). Season the rice with salt and pepper, stir well, and bring to a boil. Reduce heat, place cover on the pot, and cook until rice is just cooked through, about 14 to 16 minutes.
While the rice is cooking, place cilantro, garlic and pine nuts in a food processor and process until coarsely chopped. With the motor running, add the oil and process until smooth. Add the cheese and process until incorporated. Season with salt and pepper, to taste.
Place rice and beans in a large bowl, fold in the cilantro pesto, and garnish with the additional chopped cilantro.