Before you start, preheat oven to 220°C (or 200°C fan bake).
Pat chicken dry and cut into steaks. Place your hand flat on top of chicken and cut through horizontally. Prep garlic. Toss chicken in a large bowl with garlic and mustard. Season with salt and pepper and leave to marinate.
Prep broccoli and toss with oil on a lined oven tray. Season with salt and pepper and sprinkle over first measure of Parmesan. Bake on upper oven rack for 12-15 minutes, until tender and golden.
Heat oil in a large fry-pan on medium-high heat. Cook chicken for 3-5 minutes each side (depending on thickness), or until cooked through. Rest, covered, for 3 minutes.
Cut buns in half and place back together on an oven tray. Place on lower oven rack and cook for about 6 minutes, until warm and toasted.
Prep lettuce, tomato and avocado.
Serve buns filled with chicken, lettuce, tomato, avocado, Parmesan and Caesar dressing. Serve broccoli on the side.