Heat broiler of your oven. Place bread slices on a baking sheet. Brush top sides of bread with 2 Tablespoons of oil (divided among the 6 slices). Season with salt and pepper. Broil until golden, approximately 2 minutes.
In a large nonstick skillet, heat 1 Tablespoon olive oil over medium. Add spinach and sauté until cooked and wilted. Turn off heat and mix in goat cheese and diced avocado.
Top each slice of toast with equal amounts of the spinach/avocado/goat cheese mixture.
Heat remaining Tablespoon of oil over medium heat. Crack eggs into skillet; season with pepper. Cook until whites are almost set, about 1 minute. Cover, and remove from heat; let stand until whites are set but yolks are still soft, about 3 minutes.
Top each "avocado toast" with a cooked egg and serve.