1. Puree basil, garlic and oil in mini processor until very smooth. Season pistou to taste with salt and pepper. (Or, pull out the store-bought jar of Pesto)
2. Add enough water to medium skillet to measure 1-1/4 inches. Sprinkle salt generously into water. Bring water to simmer over medium heat. Crack eggs 1 at a time and gently slip into water. Cook until eggs whites are just set and egg yolks are still runny, about 3 minutes. (Or, cheat and use an egg poacher).
3. Place hot toasts on plates. Top each with Parmesan. Using slotted spoon, transfer 2 eggs, well drained, to each piece of brioche. Sprinkle eggs with salt and pepper. Drizzle with some of the pistou and serve.

20 minutes prep time. Serves 2.