Grease a 9×5-inch loaf pan. Cut bread slices into 1-inch pieces. Pour into prepared loaf pan.
In a medium bowl, combine eggs, eggs yolks, sugar, milk, sweetened condensed milk, and vanilla. Beat with a whisk until mixed. Pour over bread in the pan. Push bread down into the mixture to completely coat.
Pour 2 cups hot tap water into insert pan. Carefully set filled loaf pan in water.