In a mixing bowl, beat together the eggs, milk, brown sugar alternative, ground cinnamon, and vanilla extract. Then pour half of it over the bread, flip the bread over, pour the remaining on top. If you cannot fit all of the bread into the baking dish use two baking dishes, another shallow dish or bowl, or soak the bread in batches. Allow the bread to soak for up to a half hour as the more of the liquid that is absorbed, the better the results (according to some..). Place the bread on the warm skillet, sprinkle some of the churro seasoning on each side, and cook well on both sides until the bread begins to turn brown.