In a wide, shallow bowl, whisk together the eggs, milk, vanilla extract, cinnamon, sugar, and salt until well combined.

Submerge the bagel halves in the custard mixture, allowing them to soak for approximately 2 minutes per side until fully saturated.

Melt the butter in a large non-stick skillet or griddle over medium heat until foaming.

Place the soaked bagel halves cut-side down in the skillet.

Cook for 3 to 4 minutes until the cut surface is golden brown and slightly crisp.

Flip the bagels and cook for an additional 2 to 3 minutes on the outer side.

Remove from heat and serve immediately with maple syrup and optional toppings.