Heat a grill pan over medium-high heat. Brush the bread with some olive oil and season with salt and pepper. Grill until nicely toasted on both sides.
Meanwhile, heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add the mushrooms, peppers and red pepper flakes. Season with salt and pepper and cook until the vegetables are just starting to brown, a few minutes. Add the tomatoes and bring to a simmer. Add some water if it is too thick.
Using a large metal spoon or ladle, form 6 evenly spaced divots in the sauce. Crack an egg into each divot and season with salt and pepper. Cover and simmer until the eggs are cooked to your liking.
Spoon some sauce over each slice of bread and top with an egg. Drizzle with olive oil.