Pat the pork dry. Toss with 1 tablespoon soy sauce and the white pepper; let sit 10 minutes.
Whisk the 3 tablespoons soy sauce, hoisin, rice vinegar, brown sugar, water, and 1 tablespoon cornstarch in a small bowl. Set aside.
Preheat the air fryer to 400°F (200°C) for 3 to 5 minutes.
Toss the pork with ⅓ cup cornstarch until coated, adding more if needed. Let sit 5 minutes, then shake off excess.
Spray the basket. Arrange the pork in a single layer, working in batches. Spray the tops well. Air fry 8 to 10 minutes, shaking halfway, until golden and the pork reaches 145°F.
Meanwhile, heat the oil in a large skillet over medium heat. Cook the garlic, ginger, and red pepper flakes for 30 seconds. Add the green beans and carrots; cook 3 to 4 minutes until the beans are hot.
Stir the sauce, pour it into the skillet, and simmer 1 to 2 minutes until thick and glossy. Remove from heat and stir in the sesame oil.
Add the crispy pork and toss to coat. Serve immediately over rice, garnished with green onions and sesame seeds.