Drain the tofu, wrap in paper towels and place on a sheet pan or cutting board with something heavy (like a skillet) on top to dry it out, and let sit for 10 minutes.
Make the marinade by combining the tamari, rice vinegar, and ginger in a small bowl. Cut the tofu into 1-inch pieces and place in a food storage bag with the marinade. Let marinate for 30 minutes. Can be done ahead up to 24 hours.
Gently toss the tofu with 3 tablespoons of cornstarch until evenly coated.
Preheat air fryer to 375°F. Spray the basket with oil, place the tofu in an even layer in the air fryer and spray with a little more oil. Air fry for 9 minutes, shaking the basket every 3 – 4 minutes.
Toss the broccolini with oil, push the tofu to the side and add the broccolini to the air fryer. Air fry for another 6 minutes.
While the tofu and broccolini finish, heat the teriyaki sauce in a small saucepan until it simmers. Whisk the remaining tablespoon of cornstarch with 1 tablespoon of water. Whisk into the teriyaki sauce until thickened. Let cool slightly.
Toss the tofu with the thickened sauce and serve with the broccolini over rice. Garnish with furikake if desired.