Preheat broiler. In a large skillet heat olive oil and butter over medium-high heat. When butter has melted, add mushrooms and garlic. Cook 6 minutes or until mushrooms are tender and brown, stirring occasionally. Remove from heat. Season to taste with thyme, salt, and black pepper. Transfer to a bowl.
In the same skillet heat 1 tsp. olive oil over medium heat. Break eggs into skillet. Reduce heat to low; cook eggs 3 to 4 minutes or until whites are completely set and yolks start to thicken.
Meanwhile, arrange bread slices on a baking sheet. Broil 4 inches from heat for 1 minute on each side or until toasted. Place a slice of cheese on each bread slice; broil 1 minute more or until cheese melts and starts to bubble. Remove from oven. Top cheese with mushroom mixture and eggs. Sprinkle with fresh herbs or microgreens.