In a medium shallow bowl, whisk together the cornstarch, sugar, nutmeg, and salt. Add the eggs and whisk vigorously until well combined, then whisk in the milk and vanilla to make a homogenous batter.
Cut each slice of bread into three or four strips each; they should be about 1" wide.
Working with a few strips of bread at a time, soak them in the batter for about 1 minute, flipping halfway through. The bread should be thoroughly soaked but not so soggy that it’s falling apart. Remove the strips from the batter, letting any excess drip back into the bowl, and transfer to the prepared baking sheet. Repeat until you’ve used all the bread.
Bake the French toast sticks for 10 to 14 minutes, until the bottoms are deeply brown. Use an offset spatula or other thin metal spatula to unstick and flip each stick over, then break the remaining 1 tablespoon (14g) softened butter into small pieces and distribute across the pan. Allow the butter to melt briefly, then tilt the pan so it spreads and coats the surface.
Return the baking sheet to the oven for 6 to 8 minutes, until the French toast sticks are golden brown on the bottom side.
Remove the French toast sticks from the oven, and while they’re still warm, transfer them to a large bowl, sprinkle liberally with Maple Cinnamon French Toast Sugar, and toss to coat. Serve warm, with maple syrup for dipping.
Let any leftover French toast sticks cool completely, then transfer to a freezer-safe bag and freeze for up to 2 months. To reheat the French toast sticks, place them on a parchment-lined baking sheet and heat at 375°F for 10 to 15 minutes, until warmed through (no need to thaw first).
