Preheat the air fryer to 375°F (190°C) for 5 minutes.
Pat the chicken breasts dry with paper towels.
In a small bowl, mix 1 tablespoon olive oil, garlic powder, paprika, 1/2 teaspoon salt, and 1/4 teaspoon black pepper.
Brush the seasoning mixture evenly over both sides of the chicken breasts.
Place the chicken breasts in the air fryer basket in a single layer.
Cook the chicken for 10 minutes.
While the chicken cooks, toss the broccoli florets with 1 tablespoon olive oil, 1/4 teaspoon salt, and 1/8 teaspoon black pepper in a bowl.
After the chicken has cooked for 10 minutes, open the air fryer and add the seasoned broccoli around the chicken breasts.
Continue cooking for an additional 8 minutes, shaking the basket halfway through to ensure even cooking.
Check the internal temperature of the chicken breasts with a meat thermometer; it should read 165°F (74°C). If not, cook for an additional 2-3 minutes.
Remove the chicken and broccoli from the air fryer and let the chicken rest for 3 minutes before serving.