Preheat oven to 350°.
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. Cut into 6 equal portions.