Preheat oven to 350 degrees F.
Slice the root end off the entire head of garlic and the shallots, and turn them upside down, wrapping them in aluminum foil and molding the foil so it supports them to allow the cut ends to stand upright in the oven. Pour olive oil on the garlic and shallots so it slips between the skin and the cloves and wrap with the foil so it is enclosed. Roast for about 1 hour and set aside until they are cool enough to handle.
Gently squeeze the roasted garlic cloves and shallots from the skins onto a small plate. Through the feed opening of a running blender add, 1 at a time, rice vinegar, mustard, thyme, salt, pepper, roasted garlic cloves and roasted shallots. Then, leaving the blender running, add the olive oil in a slow stream. Taste the dressing and add salt and pepper, as needed.
In a mixing bowl, toss the greens with the onion, scallions, and cucumber. Fold in the tomatoes. Transfer to serving dish and top with avocado wedges, garlic stuffed-olives, and hard boiled eggs.
Recipe courtesy of Robert Irvine with Brian O'Reilly, copyright 2007 Harper Collins Publishers.