Whisk eggs, half and half, pumpkin, cinnamon, vanilla extract, pumpkin pie spice, and walnuts together in a bowl. Soak one slice of bread at a time in the pumpkin mixture, then place in the prepared skilled. Repeat with the remaining slices of bread. Stir the pumpkin mixture between dips to keep the walnuts from settling. Cook the bread until golden brown, about 3 minutes on each side.