In a shallow bowl whisk together eggs, milk, sugar, salt, cinnamon if using, and vanilla bean paste. Keep aside.
Melt 2 tbsp. of butter in a medium skillet over medium heat. Add the apples to the pan and sprinkle with brown sugar. Caramelize the apples for 7-8 minutes stirring frequently. Once done the apples should be crisp-tender. Squeeze a bit of lemon juice if you like. Do not overcook the apples or they will become mush.
In another medium skillet, melt the remaining butter over medium heat. Take the stale bread slices and dip into egg mixture for 30 seconds on each side. Its highly important for the bread to be stale otherwise it will began to fall apart once you dip it. Fry the bread slices until golden brown about 1-2 minutes, then flip to cook the other side.
Top the French toast with caramelized apples and then drizzle with maple syrup. If you like you could also top the caramelized apple French toast with lightly sweetened whipped cream.