To a bowl, add the eggs, milk, vanilla, and cinnamon. Give that a good whisk.
Add the slices of bread and make sure they get a generous soaking.
Heat a large skillet on medium heat and toss in the oil. Let that heat up for a minute or so, then lay in the soaked bread. Cook for a few minutes on each side, or until they are cooked through. Remove the French toast from the skillet and set them aside.
Wipe the skillet clean, then bring the skillet back to the burner, and set it to low, to medium heat.
Spread the Dijon mustard on one slice of the French toast, and set it into the skillet, mustard side up. Lay a slice of the Swiss cheese on top, then the ham, then another slice of cheese, and top it with the remaining slice of French toast.
Cook on low heat, and place a cover over the skillet. Cook for a few minutes on one side, then remove the cover, and flip it over. Your goal is to heat everything through and get that cheese to melt.
When you are ready to plate, remove the sandwich from the skillet, slice in half, and sprinkle a bit of powdered sugar over the top.