In a large pot, bring the rice and water to a boil. Reduce heat to low, cover, and simmer 45 minutes.
Preheat the grill for high heat.
Using a food processor, grind the toasted cashews and sunflower seeds to a fine meal. Transfer to a large bowl. Pulse the onion and carrots in the food processor until finely shredded, and mix with the ground nuts. Place the cooked rice and olive oil in the food processor, and pulse until smooth. Mix into the bowl. Season with salt. Form the mixture into patties.
Oil the grill grate. Grill the patties 6 to 8 minutes on each side, until nicely browned.