Place whole egg and egg yolk in a bowl. Add coconut milk, sugar, vanilla extract, and nutmeg; whisk until batter is combined.
Soak bread halves in batter, tossing every 2 to 3 minutes to ensure they are absorbing the batter evenly, 15 to 20 minutes.
Melt butter in a skillet over medium heat. Place soaked bread in a single layer in the skillet. Cook until richly browned, crispy, and cooked through, 5 to 7 minutes per side.
Toast coconut flakes in a dry skillet until golden brown, 3 to 5 minutes. Sprinkle over bread.
Use a French country loaf rather than a baguette to get nice big slices. Italian bread can be substituted for the French bread if preferred.
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