Place the cut chicken pieces into a gallon-size resealable bag and set aside.
In a medium saucepan, whisk together chicken broth, orange zest, orange juice, white vinegar, soy sauce, sugar, dried ginger, grated onion, minced garlic, Sriracha (if using), and pepper until combined.
Measure out 2/3 cup of the sauce mixture and pour it into the bag with the chicken; seal the bag, press out excess air, and press the chicken into the marinade. Refrigerate for 30 minutes.
Meanwhile, bring the remaining sauce in the saucepan to a gentle boil over medium heat, stirring frequently.
Whisk 2 tablespoons cornstarch with 2 tablespoons cold water in a small bowl, then stir this slurry into the simmering sauce. Reduce heat to medium-low and cook 1–2 minutes, stirring constantly, until thickened, then remove from heat.
Pour oil into a large heavy pot or Dutch oven to a depth of 1½–2 inches and heat to 350°F (use a thermometer to check).
Whisk the eggs in a shallow dish. Place 1¼ cups cornstarch in a separate shallow dish for dredging.
Remove the chicken from the marinade and discard the marinade. Working in batches, dip chicken pieces into the beaten eggs, then coat evenly with cornstarch.
Carefully add about one third of the coated chicken to the hot oil and fry 5–7 minutes until golden brown, turning once. Remove with a skimmer and drain on a paper towel–lined baking sheet. Repeat with remaining chicken in two more batches.
Place the drained fried chicken into a large bowl and toss with the prepared orange sauce until evenly coated.
Serve the orange chicken warm over rice and garnish with chopped green onions and sesame seeds if desired.
