Start by seasoning the chicken cubes with kosher salt and black pepper. In a bowl, combine the beaten egg and flour, then dip each piece of chicken into the mixture until fully coated.
Heat 3 tablespoons of olive oil (or sesame oil) in a large skillet over medium-high heat. Once hot, add the coated chicken pieces in batches, cooking until golden brown and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining oil and toss in the sliced shallots and broccoli florets. Sauté for about 3-4 minutes until the vegetables are tender but still vibrant in color.
In a separate bowl, whisk together the pomegranate juice, soy sauce, honey, rice vinegar, grated garlic, fresh ginger, crushed red pepper flakes, star anise, and bay leaf. Pour this mixture into the skillet with the vegetables, stirring to combine.
Return the cooked chicken to the skillet, tossing to coat it in the sauce. Allow everything to simmer together for another 5 minutes, letting the flavors meld beautifully.
While the chicken is simmering, prepare the ginger rice. Cook rice according to package instructions, adding freshly grated ginger to the water for extra flavor. Once done, fluff the rice with a fork and serve it alongside the spicy chicken mixture. Top with toasted sesame seeds and sliced green onions for a burst of freshness.