Preheat the oven to 350°. Coat the bottoms and sides of eight 4-ounce ramekins with 1 teaspoon of olive oil each. Arrange the ramekins around the sides of a roasting pan and crack 1 egg into each one. Top each egg with 1/2 tablespoon of butter and season with salt and pepper. Pour enough boiling water into the roasting pan to reach halfway up the sides of the ramekins.
Bake the eggs in the oven for about 15 minutes, turning the pan halfway through cooking, until the yolks are runny and the whites are just firm. Garnish the eggs with the chopped basil and serve right away with buttered toast.