Preheat oven to 300 degrees F. Place the slices of bread on a wire rack set in a rimmed baking sheet. Bake 16 minutes, flipping halfway through cooking, until almost dry throughout. Remove and let cool 5 minutes. Reduce oven temperature to 200 degrees.
Whisk milk, egg yolks, sugar, melted butter, vanilla, cinnamon, and salt in a large bowl. Transfer to a 9 X 13 inch baking dish.
Soak bread in milk mixture until saturated but not falling apart, about 20 seconds each side. Using a slotted spatula pick up one slice at a time allowing excess milk mixture to drip off. Place soaked bread on a baking sheet or platter.
Preheat electric griddle to 350 degrees F. Spray griddle with non-stick cooking spray or melt some butter on the griddle. Use a slotted spatula to transfer slices of bread to the griddle. Cook until golden brown, 3 to 4 minutes. Flip and continue to cook until the second side is golden brown, 3 to 4 minutes longer. Transfer to a baking sheet and place in warmed oven. Repeat using the remaining bread. Serve warm.