Divide the carrot and cucumber ribbons into two re-sealable containers (16 ounce mason jars work great for this). In a bowl, stir together the water, rice vinegar, agave nectar, salt and pepper. Pour this mixture over the vegetable ribbons, dividing it evenly between the two containers. Seal the containers and gently shake them a couple of times. Then transfer the containers to your refrigerator to chill for 1 hour. A longer refrigeration time is okay, too.
Meanwhile, cook the brown rice according to the package instructions. In a small bowl, combine the rice vinegar, tamari and salt. Then, while the cooked rice is still slightly warm, drizzle this dressing over the rice, tossing with a fork to combine. Set aside.
Assemble the sushi bowls:
Divide the rice evenly between 4 bowls. Top with some of the quick-pickled vegetables, mango, edamame and scallions. Sprinkle with sesame seeds. Serve immediately.