Preheat the oven to 475° F. Line a baking sheet with parchment paper or grease with oil.Add the chicken, egg, and a pinch of pepper to a bowl. Toss to combine. Add the flour to another bowl. Dredge the chicken in batches through the flour, tossing to coat. Place the chicken on one side of the prepared baking sheet. Drizzle with 2 tablespoons of oil. Add the broccoli and shallots to the other side of the pan and toss with 2 more tablespoons of oil, salt, and pepper. Bake for 12 minutes. Toss the broccoli, flip the chicken, and return to the oven another 3-5 minutes, until the chicken is cooked through.Meanwhile, in a large skillet, combine the pomegranate juice, soy sauce, honey, rice vinegar, garlic, ginger, star anise, bay leaf, and red pepper flakes. Set over medium-high heat and bring the sauce to a boil. Boil 5-8 minutes, until the sauce thickens and reduces by about 1/Stir in the chicken, broccoli, and sesame seeds. Cook until the sauce coats the chicken. Serve the chicken, broccoli, and sauce over bowls of ginger rice (recipe in notes) topped with green onions.