Preheat the oven to 200°C top/bottom heat.
Boil the potatoes until they're cooked through.
Peel and dice the onion.
Peel and crush the garlic.
Cut the broccoli florets from the stem.
Peel the carrots and cut them into Paysanne (as you like).
Blanch the carrots and broccoli. Cook them in boiling salted water for 1 min, then immediately shock them in cold or ice water to keep their color fresh and the vegetables nice and crisp.
Peel the garlic, chop it finely, and set aside.