In a medium-size bowl beat together the eggs and the milk. Then beat flour, powdered sugar, vanilla, and salt into the egg mixture. Strain the custard mixture using a wire mesh strainer into another bowl.
Heat a skillet or a griddle to about 350 degrees. Brush the skillet/griddle with butter. Place the bread into the custard mixture, then flip over the bread, and then place the bread onto the hot cooking surface. Cook for 1 to 2 minutes on each side. The bread should be golden in color when cooked through. Remove from skillet. Cut the toast diagonally, and sprinkle with powdered sugar, and top with butter.