Heat the oven to 200ºC/ 180ºC fan/gas 6 and oil 2 large baking trays. Peel and halve the parsnips, then mix the wholegrain mustard, lemon juice, honey, thyme and plenty of salt and pepper in a bowl. Toss the chicken and parsnips through the marinade, divide evenly between the baking trays (give the chicken and parsnips a bit of space), then bake for 30 minutes.
Drizzle the tenderstem broccoli with a little olive oil and add to the trays, tossing everything so the pieces all brown evenly. Cook for another 15 minutes until the chicken thighs and parsnips are blackened and caramelised, and everything is cooked through. Serve with lemon wedges.