In a large bowl, combine all citrus juices, sesame oil, canola oil, ginger, garlic, and a pinch of salt. Add the carrots and cabbage and toss to coat. Let sit 10 minutes. Add the scallions, cilantro, sesame seeds, and salt to taste.
Meanwhile, heat the broiler with the oven rack in the highest position. In a medium bowl, whisk together the honey, soy sauce, and red pepper flakes until the honey has completely dissolved. Add the shrimp and toss and let sit 10 minutes. Arrange the shrimp on a large parchment lined baking sheet and broil 2-3 mins per side on the highest rack, or until the shrimp are pink and opaque throughout. (There will be a tiny bit of smoke from the soy, don’t worry, it’s normal!)
Serve the shrimp and citrusy cabbage with the brown rice.