Whisk together the eggs, milk, sugar, cinnamon, and vanilla extract in a shallow bowl.
Cut 3.5-4 inch rounds out of each slice of bread using a cookie cutter.
Dip the bread slices into the egg wash, coating both sides. Transfer to a plate.
In a small dish, mix together the remaining sugar and cinnamon, and set aside.
Heat a medium non-stick skillet with ½ tablespoon of butter.
Working in batches, fry the coated bread slices on medium-low heat on each side until golden. Once golden, immediately dip each French toast slice into the cinnamon sugar mixture to evenly coat (using tongs). Repeat with remaining toasts. Transfer to a plate and allow to cool slightly.
Onto 6 slices of churro toast, add a scoop of ice cream or gelato, then top with another slice of churro toast. Gently press down to form a sandwich. Instead of using scoops of ice cream, you can also cut ½-inch thick discs straight out of the ice cream pint, removing the carton wrapper as you go.