Preheat oven to 400°F (200°C).
Steam the broccoli: Add broccoli and 2 tablespoons of water to a microwave-safe bowl. Cover and microwave for 2 minutes. Drain and finely chop.
Prepare the filling: In a mixing bowl, combine chopped broccoli, shredded cheddar, cream cheese, chives, salt, and pepper. Stir until smooth and evenly mixed.
Stuff the chicken: Using a sharp knife, slice a deep pocket into the side of each chicken breast without cutting all the way through. Fill each pocket generously with the broccoli-cheddar mixture.
Season the chicken: Rub the outside of each breast with garlic powder, cumin, additional salt and pepper, and any other desired spices.
Sear: Heat 2 tablespoons olive oil in each of two oven-safe skillets over medium heat. Sear two chicken breasts per pan, about 3 minutes per side, until golden.
Bake: Transfer the skillets to the oven and bake for 10–15 minutes, or until the internal temperature reaches 165°F (74°C).
Rest and serve: Let the chicken rest for 5 minutes before serving to retain juices. Serve warm.