In a bowl, whisk together eggs, half-and-half, and nutmeg until smooth. Pour mixture into a shallow pan.

Place slices of banana bread into the egg mixture. Allow the bread to soak up egg mixture for 30 seconds. Turn and do the same for the other side.

Place grated coconut on a plate. Remove soaked bread from pan, place onto dessicated coconut. Turn and coat the other side.

Heat butter in a large non-stick pan on medium heat. Transfer bread to pan and cook for about 2 to 3 minutes on each side.

Serve immediately with maple syrup, if desired.