Rinse the sushi rice under cold water until the water runs clear. Combine the rice and water in a medium saucepan and bring to a boil. Once boiling, reduce the heat to low, cover, and simmer for 18-20 minutes until the rice is tender and water is absorbed. Remove from heat and let it sit, covered, for 10 minutes.

While the rice is cooking, prepare the teriyaki sauce by combining soy sauce, honey, rice vinegar, and sesame oil in a small saucepan. Bring to a simmer over medium heat, stirring occasionally, until the sauce thickens slightly, about 5-7 minutes. Remove from heat and set aside.

In a large skillet over medium-high heat, add the shrimp. Season with salt and pepper and cook for 2-3 minutes on each side until they turn pink and opaque. Pour half of the teriyaki sauce over the shrimp and toss to coat. Remove from heat.

To assemble the bowls, divide the cooked sushi rice among four bowls. Top each bowl with the teriyaki shrimp, avocado slices, cucumber, shredded carrots, and green onions.

Drizzle the remaining teriyaki sauce over the bowls and sprinkle with sesame seeds. Serve immediately.