Cook rinsed basmati according to its package, fluff and spread on a shallow tray so steam can escape.
Heat oven to 425°F and prepare separate rimmed sheet pans for chicken and broccoli.
Mix 3 tablespoons oil, lemon zest, garlic powder, oregano, paprika, 3/4 teaspoon salt and 1/2 teaspoon pepper.
Pound chicken to an even 3/4-inch thickness, pat dry and coat both sides with two-thirds of the seasoning oil.
Toss broccoli with remaining oil, seasoning mixture, salt and pepper and spread in one layer on the second pan.
Bake, turning broccoli at 12 minutes; remove broccoli when browned and each chicken piece when its thickest center reaches 165°F.
Rest chicken 8 minutes; loosen the warm pan with broth and stir in lemon juice and resting juices.
Slice across the grain, divide rice, broccoli and chicken among six containers and spoon pan juices over chicken and rice.
