Bring the beef stock to a boil in a large saucepan. Add the leeks, cover and simmer over low heat, turning a few times, until tender, about 5 minutes. Using a slotted spoon, transfer the leeks to a large glass baking dish and cover with foil. Repeat with the remaining vegetables, cooking the pearl onions and carrots for 12 minutes, then the broccoli for 4 minutes and the zucchini for 2 minutes. Discard the strings from the leeks and cut them crosswise into 1-inch lengths, keeping the pieces intact. Re-cover the baking dish with foil. Keep the stock covered.