Prepare the Pan & Oven: Adjust your oven rack to the middle position and preheat to 420°F (215°C). Lightly coat a large 13x18-inch rimmed baking sheet with the neutral cooking oil.
Marinate the Chicken: In a medium-sized bowl, thoroughly combine the low-sodium soy sauce, rice vinegar, sriracha, toasted sesame oil, minced garlic, minced ginger, and smoked paprika. Add the cubed chicken to the marinade, ensuring each piece is well-coated. Cover the bowl and allow the chicken to marinate in the refrigerator for at least 15 minutes, or up to 30 minutes. While the chicken is marinating, proceed with chopping your vegetables.
Combine Ingredients on Pan: Scatter the riced cauliflower evenly across the prepared baking sheet. Distribute the chopped carrots, green peas, and diced red bell pepper over the cauliflower. Arrange the marinated chicken pieces amongst the vegetables, then pour any remaining marinade from the bowl over the entire mixture.
Initial Bake: Gently toss all the ingredients on the baking sheet with tongs to ensure everything is lightly coated with the marinade and oil. Spread the mixture into a single, even layer. Transfer the baking sheet to the preheated oven. Bake for 30-35 minutes, removing the pan halfway through (around 15-17 minutes) to stir the contents for even cooking.
Incorporate the Egg: After the 30-35 minute baking period, take the pan out of the oven. Using a spatula, push the cauliflower and chicken mixture towards the outer edges of the baking sheet to create a clear, open space in the center. Lightly whisk the large egg in a small bowl and pour it into this cleared space.
Cook Egg & Finalize: Return the baking sheet to the oven and bake for an additional 3-5 minutes, or just until the egg is set but not overly dry. Remove the pan from the oven. Use your spatula to break the cooked egg into small, scrambled pieces.
Serve: Gently toss the scrambled egg pieces with the rest of the chicken and cauliflower mixture until it's well distributed. Sprinkle the freshly sliced green onions over the top. Serve warm.