Lightly butter one side of each slice of bread and leave it butter-side-down on the plate while you assemble the sandwich.
For each sandwich, spread fruit preserves on one slice of bread, dijonnaise on the opposite slice of bread, add a layer of cheese to the dijonnaise, add a few slices of ham on top of that, and place the fruit preserve slice on top so the buttered side is on the outside of the sandwich.
For best results, place a layer of parchment paper over the sandwiches, place a cast iron skillet on top of the parchment paper to press the sandwich together. Leave this on the sandwich for about 5 minutes. Remove pan and parchment paper when finished.
In a medium shallow bowl, whisk together eggs, sugar, heavy cream, milk, vanilla (and cinnamon, optional) until combined. Dip the sandwich in the batter, soaking it for only a few seconds on each side.
Preheat oven to 350F/175C.
Preheat the skillet over medium heat. Melt about 1 tablespoon of butter in a skillet pan (swirl it around so it coats the pan bottom evenly) along with 1 tablespoon of oil.
Transfer sandwich to the hot skillet, cooking each sandwich one at a time. Cook until golden brown, 1-3 minutes on each side. You may need to add a little more butter and oil before cooking each additional sandwich.
Once each sandwich has been cooked to golden perfection on both sides, place it on a parchment-lined sheet pan. Once all sandwiches have been cooked on the stove, place them in the oven at 350F/175C for 10-20 minutes or until desired gooey, cheese-y insides have been achieved.
Cut sandwiches diagonally and serve immediately with your favorite toppings and dipping sauces: maple syrup, jam, powdered sugar, fruit, etc.