Bring 1 cup water and the rice to a boil in a small saucepan over medium-high heat. Cover and reduce the heat to medium low; cook until the liquid is absorbed and the rice is tender, about 30 minutes. Remove from the heat and let sit, covered, 3 minutes. Season with salt and let cool.
Meanwhile, mix the peanut butter, hoisin sauce, Sriracha and 2 teaspoons water in a small bowl; set aside.
Lay out a large piece of plastic wrap. Very thinly slice 1 avocado lengthwise and fan out in 2 overlapping rows on the plastic wrap to form a 6-by-9-inch rectangle. Position the plastic wrap so the long side of the avocado rectangle is closest to you. Spread half the peanut sauce in a line across the center of the avocado rectangle from left to right, then spread 1/2 cup rice over the sauce. Top with a single line each of cucumber, bell pepper and mango (3 strips each). Season with salt and squeeze some lime juice over the top.
Starting from the bottom long edge, roll up the avocado tightly into a log using the plastic wrap to help you. Slice the roll through the plastic wrap into 3/4-inch-thick rounds, then remove the plastic.
Repeat to form another roll. Squeeze more lime juice over the rolls.