Peel the carrots, separate the broccoli florets and cut the zucchini into strips lengthwise. Add water to three pots and a pinch of salt and cook the vegetables separately.
Drain on absorbent paper towels.
Place the eggs in a container, chop 5 cooked carrots and blend with an electric mixer until evenly puréed.
Put a strip of baking paper over the baking dish, rub with a little butter and sprinkle with breadcrumbs.
Place a layer of the purée over the baking dish, cut the remaining 2 carrots into strips, place them in the dish, pour another bit of the purée, add the broccoli florets, a little purée, cover with slices of zucchini, and then pour the rest of the purée. Place in the oven in a bain-marie at 160°C for 45 minutes. Leave to cool down and remove from the baking dish.
Serve with a little mayonnaise and sprinkle with a little chopped parsley.