Serious Eats: Recipes
French Toast Bagels
I used a nonstick skillet, but Molly from the blog Orangette has said that oil makes for the superior 'finish' on any French toast recipe.
Very stale bagels might require a longer marinade in the milk and egg mixture.
For stuffed French toast, I'd suggest assembling the sandwiches after the bagel halves cook in the skillet, given that turning them with the cream cheese is unwieldy and the cheese cooks before the bagel slices. The steam from the cooked bagels will melt the cheese just enough.
Note: If using a nonstick skillet, you may omit the butter or oil if desired.