In a large shallow bowl, using a fork, beat the eggs until lightly frothy. Stir in the milk and set aside. Peel the bananas into a small bowl and mash them with a fork. Stir in the walnuts and the nutmeg.
Spread the banana mixture over 4 of the bread slices, leaving a 1/4-inch border uncovered on all edges. Top with the remaining bread slices and press down gently to seal.
Place 2 sandwiches in the egg mixture and press down gently. Turn over and let soak for a moment until evenly saturated on both sides. Repeat with the other 2 remaining sandwiches.
In a frying pan or on a griddle melt butter over medium heat. Place the sandwiches in pan or on griddle and fry until the undersides are golden brown, about 2 minutes. Flip the sandwiches with a spatula, adding more butter to the pan if needed, and fry until golden brown.
To serve place the toast on plates and dust with powdered sugar. Serve with maple syrup or jam.
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