Prep the chicken: Pat the chicken breasts dry.
If they’re thick on one end, slice horizontally to create cutlets or pound to an even 1/2-inch thickness. Even thickness cooks more evenly and stays juicier.
Make the marinade: In a bowl, whisk 1 tablespoon olive oil, lemon zest, half the lemon juice, garlic, salt, pepper, paprika, and dried herbs. Toss the chicken in the mixture until coated. Let sit for 15–30 minutes at room temperature, or up to 4 hours in the fridge.
Preheat the grill or pan: Heat a gas grill to medium-high, or warm a grill pan or cast-iron skillet over medium-high until hot.
Lightly oil the grates or pan to prevent sticking.
Grill the chicken: Place the chicken on the hot surface. Cook 4–6 minutes per side, depending on thickness, until the internal temperature reaches 165°F (74°C). If using a skillet, lower the heat slightly after searing to avoid burning spices.
Rest the chicken: Transfer to a plate and tent loosely with foil.
Rest for 5 minutes to lock in juices.
Steam the broccoli: While the chicken rests, add 1 cup water to a pot and bring to a simmer. Place broccoli florets in a steamer basket, cover, and steam 4–5 minutes until crisp-tender. If you don’t have a steamer, add 1/4 inch water to a skillet, cover, and simmer until just tender.
Season the broccoli: Transfer to a bowl and toss with 1 tablespoon olive oil or a pat of butter, a pinch of salt, and the remaining lemon juice.
Add red pepper flakes or Parmesan if you like.
Serve: Slice the chicken across the grain. Plate with broccoli and spoon over any juices from the resting plate. Finish with an extra squeeze of lemon and a crack of black pepper.