Prep: Preheat the oven to 375°F.
Steam Broccoli: Add the broccoli florets and two tablespoons of water to a large microwaveable safe bowl. Cover with a damp paper towel and microwave for 2 minutes. Drain the excess water. Push the broccoli to one side and add the remaining filling ingredients to the opposite side. Set aside without mixing.
Filling: Whisk the Spice Rub together in a small bowl. Remove one teaspoon and add it to the filling ingredients. Mix the cream cheese side until thoroughly combined, then fold in the broccoli.
Tenderize: Lay the chicken on a cutting board and top with plastic wrap. Pound a few times with a meat mallet or side of a can to tenderize. Remove the plastic wrap and pat the chicken dry with paper towels.
Make Pocket: (Slice the thicker, rounder side of the chicken—see How To Make Pics in the post). Slice through the equator *but do not cut all the way through* to create a deep pocket in each chicken breast.
Stuff Chicken: Stuff each breast with the filling (I find it easiest to squeeze the filling with my hand and then stuff it in). If the filling is falling out, secure it with toothpicks.
Season: Sprinkle and pat the Spice Rub evenly over each side of the chicken.
Sear: Heat a large cast iron skillet over medium-high heat until smoking. Add the olive oil and swirl. Sear two chicken breasts at a time, about 2-3 minutes per side, or until golden. Remove the chicken and repeat with the other two breasts.
Add all the chicken back to the pan: Add three tablespoons of chicken broth (careful, it can splatter). Cover the skillet with foil and transfer it to the oven. (If your skillet isn’t oven safe or too small to fit all the breasts, use a 9x13 baking dish.)
Bake at 375° for 12-17 minutes, or until the internal temperature of the chicken is 160°F on an instant read thermometer (chicken flesh, not the filling). Let the chicken rest for 5 minutes to rise to 165°F. Delicious with mashed potatoes!