In a large bowl, combine chicken, cornstarch, salt, and pepper together, tossing until chicken is evenly coated in cornstarch.
Heat 2 tablespoons vegetable oil in a large nonstick skillet over medium-high heat. Working in batches, add chicken to pan in a single layer, shaking off excess cornstarch, and fry on all sides until chicken is golden-brown and crispy. Cook remaining chicken, adding additional oil to pan as needed. Transfer chicken to a clean plate and set aside for a moment.
Heat remaining 1 tablespoon vegetable oil in same skillet over medium-high heat. Add onion and broccoli and saute until crisp-tender, about 3-5 minutes. Add garlic and cook 1 additional minute until fragrant.
Reduce heat to medium and add browned chicken, apricot jam, soy sauce, and apple cider vinegar to pan. Stir 3-5 minutes over medium heat until jam is melted and the sauce is bubbly and coating the chicken and broccoli.
Season chicken and broccoli with salt and pepper to taste if needed and serve warm over hot rice with green onions on top. Enjoy!