Warm a cast iron skillet over medium heat then drizzle with olive oil. Add the mushrooms and garlic and let sauté for 3 to 5 minutes until browned. Turn the mushrooms, then let them brown for another 3 to 5 minutes. If the pan seems too dry, add a little more oil as needed.
Stir in tarragon and create two wells.
Crack in eggs and continue to cook until the egg whites are set.
While the eggs are cooking, grill or toast the artisan bread until golden.
Once the eggs are cooked, transfer them to buttered toasts with mushrooms stacked around. Season with salt and freshly cracked pepper and top with more fresh tarragon as desired.