Aioli Et Ses Legumes

3 garlic cloves1/2 teaspoon salt1/2 cup cooked warm mashed potato1 egg yolk3/4 cup olive oil8 small potatoes, peeled4 medium carrots peeled, cut in 2 x 1/4-inch strips2 medium turnips peeled, cut in 2 x 1/4-inch strips4 small leeks, trimmed, cut in 2 x 1/4-inch stripsFor the sauce: Using a mortar and pestle, mash the garlic with the salt until purEed. Mix in potato and yolk and beat in the olive oil very gradually with a whisk as though making mayonnaise. Set aside. Steam the potatoes, covered, for 5 minutes. Add carrots, turnips, and leeks. Cover and steam 8 to 10 minutes, until tender. To serve, place vegetables on a warmed platter. Keep sauce warm in a fondue pot or chafing dish.