In a small pan, combine persimmon, syrup, and lemon juice. Bring to a boil over medium heat, then lower heat to a simmer and add spices.
In a small bowl, whisk water and arrowroot flour, then stir into persimmon mixture. Continue to simmer for another 3-5 minutes until thickened and transfer to a resealable container and allow to cool before placing in refrigerator (this can be done ahead of time).
Whisk all toast ingredients except bread until smooth. Arrange sliced, dried out bread in a flat bottom dish (I used a 6 cup rectangular Pyrex dish) and pour egg mixture on top. Soak the bread for 5-10 minutes until egg mixture is absorbed but bread is not overly soggy.
Heat a griddle or skillet over medium-high heat and spray with non-stick cooking spray. Cook toast sticks in batches until golden brown on both sides. You may need to turn down heat to medium after 1st batch.
Serve French toast sticks with persimmon compote.