Heat oil in a medium nonstick skillet over medium heat. Add mushrooms and salt; stir well. Cover and cook for 5 minutes. Increase heat to medium-high; add minced thyme, flour, and pepper, and cook for 1 minute, stirring occasionally.
Rub cut sides of garlic over bread slices. Spoon 2 tablespoons mushroom mixture onto each bread slice. Garnish with thyme sprigs, if desired.