For the French toast: Preheat the oven to 300 degrees F. Mix together 1/2 cup granulated sugar and the cinnamon in a small baking dish. Put the bread on a baking rack set on a baking sheet and put it in the oven to dry out for 10 minutes. Let cool.
Whisk together the eggs, yolks, vanilla, salt, 1 cup of the milk and the remaining 2 tablespoons granulated sugar until smooth. Add half of the bread and let soak in the mixture for about 30 seconds on each side.
While the bread is soaking, melt 2 tablespoons of the butter and 2 tablespoons of the oil in a large nonstick skillet over medium heat until the mixture begins to shimmer. Fry the bread until golden brown and just cooked through, 2 to 3 minutes per side. Roll each piece in the cinnamon sugar.
Transfer the French toast to the baking rack set on a baking sheet and put in the oven to heat through for 5 minutes. Repeat the soaking and frying process with the remaining pieces of bread.
For the maple cream: whisk together the confectioners' sugar, maple syrup and 1 tablespoon milk until smooth. Add more milk a little at a time, if needed, to make a sauce that will just cling to the French toast. Wrap bunches of 3 French toast sticks in foil or paper, put some of the sauce into small containers with lids and eat on the go.