Trim the pearl onions as necessary so that they are uniform in size and will cook evenly.
Place them in two separate small saucepans. Add 1 cup of water, ½ teaspoon of the butter, and ½ teaspoon of the sugar to each pan; the water should just cover the onions.
Bring to a simmer and cook over medium heat for 20 to 25 minutes, or until the water has evaporated and the onions are tender and glazed but not browned. Remove from the heat and set aside.
One vegetable at a time, blanch the asparagus, haricots verts, and wax beans in boiling water until tender, chill in ice water; drain, and pat dry.
Blanch the carrots in boiling water or strained barigoule liquid (reserved from the artichokes) until tender; chill, drain, and pat dry.
Cut the wax beans on the diagonal into ¼ inch pieces.
Lightly toss all the vegetables in a bowl with a few drops each of extra virgin oil and balsamic vinegar.
Place 1 tablespoon of the eggplant caviar in the center of each plate. Arrange about two thirds of the artichoke hearts around the spoonfuls of caviar. Artfully arrange the remaining vegetables, including the remaining artichokes, in a stack in the center and sprinkle with gray salt.
Lightly dress the herb salad with olive oil and kosher salt and stack a small bunch on each salad.
Squeeze dots of balsamic glaze around each plate.
If desired, spoon a generous tablespoon of gazpacho around each salad at the table.