Preheat the oven to 450 degrees F.
Whisk together the half-and-half, sugar, vanilla, cinnamon and eggs. Dip the bread into the batter and let soak for 1 minute.
In a large pan over medium heat, add the butter and grapeseed oil. Add the soaked bread to the pan and fry on both sides until golden brown. Remove to a baking sheet and brush with maple syrup
Divide the ham, bacon and cheese among four of the bread slices, top with the remaining bread and place in the oven; the sandwiches are done when the cheese has melted, about 4 minutes.