Remove white papery skin from garlic head (do not peel or separate the cloves). Wrap head in foil; set aside.
Arrange mushrooms and next 5 ingredients (mushrooms through tomatoes) on a jelly-roll pan coated with cooking spray.
Sprinkle salt, thyme, and pepper over vegetables; toss well. Nestle rosemary sprigs into vegetables.
Bake garlic and vegetables at 350 for 45 minutes, stirring vegetables every 15 minutes. Discard rosemary sprigs. Separate garlic cloves, and squeeze to extract garlic pulp; discard skins. Set garlic pulp aside.
Spoon yogurt onto several layers of heavy-duty paper towels; spread to 1/2-inch thickness. Cover with additional paper towels; let stand 10 minutes. Scrape yogurt into a bowl, using a rubber spatula. Stir in garlic pulp, mustard, and vinegar; set aside.
Hollow out top and bottom halves of bread, leaving a 1-inch-thick shell; reserve torn bread for another use.
Spread yogurt mixture over top and bottom halves of loaf. Arrange vegetables on bottom half of loaf; replace top half. Wrap loaf in foil; bake at 350 for 15 minutes.