Remove and discard stems from mushrooms, reserving caps. Heat oil in a large nonstick skillet over medium-high heat. Add mushroom caps; sauté 5 minutes. Reduce heat to medium. Add sage, thyme, and garlic; sauté 3 minutes. Stir in sherry vinegar, salt, and pepper; bring to a boil. Remove from heat.
Pour mushroom mixture over spinach mixture, tossing well to coat. Drizzle with balsamic vinegar. Place about 1 cup salad on each of 4 plates; top each serving with 2 egg quarters.