Mix together the honey, mustard, and brown sugar in a small bowl.
Place the chicken breasts on a large baking tray/sheet pan. Brush the honey-mustard mixture all over the chicken breasts (it will pour off a little, that's fine).
Arrange the potatoes, carrots and onion wedges around the chicken.
Drizzle two tablespoons of the oil over the chicken and vegetables, then sprinkle on the salt and pepper. Bake in the oven for 20 minutes.
Move the vegetables around the sheet pan a little, using a spatula, and baste any juice over the chicken breasts (especially any of the mustard sauce that may have poured off the chicken).
Add the green beans to the sheet pan and cook for 5 minutes. Now add the broccoli and drizzle the remaining oil over the brocolli and the green beans. Cook for a further 5 minutes, until the chicken is cooked through and the vegetables are tender.
Slice the chicken breasts and dish out the chicken and vegetables onto four plates (no need to slice if you prefer to serve to 3 people).