Step 1: Prepare the Sushi Rice

1. Rinse the sushi rice under cold water until the water runs clear.
2. Add the rinsed rice and water to a pot and bring to a boil over medium heat. Cover, reduce heat to low, and let it simmer for 15 minutes.
3. Remove from heat and let the rice sit, covered, for another 10 minutes.
4. In a small bowl, mix the rice vinegar, sugar, and salt until dissolved.
5. Transfer the rice to a large bowl and gently fold in the vinegar mixture using a wooden spoon. Let it cool to room temperature.

Step 2: Prepare the Vegetables

1. Thinly slice the bell peppers, cucumber, carrot, mango, and avocado into uniform strips.
2. Shred the purple cabbage finely for easy rolling.

Step 3: Assemble the Sushi Rolls

1. Place a sheet of nori on a bamboo sushi mat, rough side facing up.
2. Wet your hands slightly and spread a thin layer of sushi rice over the nori, leaving a 1-inch border at the top.
3. Arrange the sliced vegetables in a horizontal line across the lower third of the rice.
4. Carefully lift the edge of the sushi mat and begin rolling the nori over the filling, applying gentle pressure to create a tight roll.

Step 4: Slice and Serve

1. Use a sharp knife dipped in water to cut the roll into even slices.
2. Sprinkle with black and white sesame seeds for added texture.
3. Serve with soy sauce, wasabi, and pickled ginger on the side.