Combine rice and water in a saucepan and bring to a boil. Reduce heat to low, cover, and cook for 20 minutes, or until tender and water is absorbed. Leave covered, and let stand for 10 minutes. Remove to a bowl to cool completely.

Heat a skillet over medium heat, and coat with cooking spray. Pour in the eggs, and scramble until cooked through. Season them with a little salt and pepper. Remove from heat and set aside.

Lay one sheet of nori on a clean work surface, or if you have one, a sushi mat. Wet your hands, and press a layer of cooled rice about 1/3 inch thick onto half of the sheet. Spread a line of pesto across the edge of the rice about 1/2 inch wide. Top with a line of egg. Roll the sheet of nori over the pesto egg and rice to reach the empty part of the sheet. Wet the end, and roll up to seal. Use a knife to cut the roll into 6 small rolls.