Heat a large Dutch oven over medium-high heat. Coat pan with cooking spray. Add celery, carrot, and mushrooms; sauté 5 minutes or until lightly browned. Remove from heat; slowly stir in 1 cup wine, scraping pan to loosen browned bits. Add broth, water, parsley, and 2 thyme sprigs. Bring to a simmer over medium heat; cook 30 minutes. Strain broth mixture through a sieve into a bowl; discard solids.
Heat pan over medium heat. Coat pan with cooking spray. Add onion and salt; cook 20 minutes or until golden brown, stirring frequently. Stir in strained broth; bring to a boil. Reduce heat, and simmer 20 minutes or until onions are very tender. Remove from heat; stir in 3 tablespoons wine and pepper.
Ladle about 3/4 cup soup into each of 8 ovenproof bowls. Place bowls on a jelly-roll pan. Top each serving with 1 bread slice and 1 1/2 tablespoons cheese. Broil 1 minute or until cheese begins to brown. Garnish with thyme sprigs, if desired. Serve immediately.