Preheat oven to 400 degrees F.
In a small bowl, combine lemon pepper, garlic powder, salt and pepper. Set aside. In another small bowl or glass measuring cup, combine lemon juice, lemon zest and chicken broth. Set aside
Cover chicken with plastic wrap or place in a gallon- size sealable bag. Pound chicken with a mallet until it is uniform in thickness (mine was about 3/4" thick). Sprinkle both sides with the lemon pepper seasoning mixture.
Melt 1 tablespoon of butter in a 12" oven-safe skillet over low heat. Turn heat to medium-high and place chicken in the skillet. Cook for about 4 minutes on one side; until chicken is golden brown. Flip chicken and sear for 2 minutes on the other side.
Turn off heat and gently pour lemon/chicken broth mixture around the chicken (not over it). Arrange broccoli pieces around the chicken in the skillet and set in the oven for 10 minutes, or until chicken is cooked through (165-175 degrees; it will feel firm and the juices will run clear when pierced with a knife).
Serve hot, spooning the sauce from the skillet over each piece as it's plated, if desired.