Combine eggs and half and half in large, shallow bowl. Beat well to combine; stir in salt and vanilla.
Soak bread in this mixture for 1 minute on each side, turning once, so the bread absorbs some of the custard.
Heat electric skillet to 350 F, or heat a large skillet on the stovetop for a few minutes.
Place about 2 tablespoons of butter in the skillet, so it melts and coats the bottom.
Lift the bread out of the custard mixture, and let drain briefly then place the bread in the skillet.
Cook the bread over medium heat, turning once, until golden brown on both sides, about 5 to 8 minutes. Serve immediately with your favorite toppings.