For the grilled brown rice burgers, heat the oil in a saucepan and sauté the finely chopped onion until soft. Add the mushrooms and let them steam for a while.
Remove the pot from the heat and mix the rice, breadcrumbs, walnuts and egg with the onion-mushroom mixture. Season with salt and pepper and knead into a firm mass. If the mass is too firm, simply add a little water.
Form about 6 burgers from the mixture with your hands and let them rest in the refrigerator for 30 minutes. Grill the burgers for 5-6 minutes on each side, brushing them frequently with oil.