Place bread cubes on a sheet pan; bake at 375°F for 13 minutes or until browned and crisp.
Rub 1/2 teaspoon oil into each of 4 (8-ounce) mini cocottes or ramekins to coat inside. Divide bread cubes among cocottes. Crack one egg into each cocotte. Season each egg with 1/8 teaspoon salt and a dash of pepper. Spoon 1 tablespoon marinara into each. Sprinkle each with 1 teaspoon feta. Place cocottes in oven; bake at 375°F for 12 minutes or until whites are set. Sprinkle with oregano. Drizzle with additional oil, if desired.