Combine the egg, milk, and vanilla extract in a shallow dish such as a pie pan. Mix well, and then dunk both sides of each Cinnabon bun half in the mixture making sure to saturate them pretty well.
Melt about a tablespoon of butter in a nonstick skillet or griddle. Cook on each side until golden brown.
Serve with a dusting of powdered sugar and/or maple syrup if desired.