In a small saucepan, combine the cherries, ¼ cup water, maple syrup, and lemon juice and bring to a gentle boil over medium heat. Mash the cherries with a potato masher or the back of a spoon.
Combine the cornstarch with 2 tablespoons water and mix well. Add to the cherry mixture, raise heat, and bring to a boil. Stir and cook until the mixture thickens, about 1 minute. Remove from heat and add the vitamin D3 drops. Let cool while making the toast sticks.
Cut the bread into thirds length-wise.
In a wide, shallow bowl or pie plate, lightly beat the eggs. Add the milk and vanilla and mix well.
Heat a large non-stick pan over medium heat, add 2 tablespoons of butter and let melt. Dip the toast sticks into the egg and milk mixture and let it get saturated. Let the excess liquid drip off and place the sticks in the hot pan. Cook in batches; do not overcrowd the pan. Cook until golden brown, about 4 minutes, and flip and cook on the other side until golden brown, another 3-4 minutes. Repeat with remaining bread sticks, adding more butter to the pan between batches.
Serve the French toast sticks with the cherry dipping sauce.