Preheat the oven to 400°F (204°C) and line a baking sheet with parchment.

In a heavy skillet, heat 1 tablespoon of butter and 1 tablespoon of vegetable oil over medium heat, or preheat an electric griddle to 300°F (150°C).

In a small bowl, whisk together eggs, heavy cream, salt, nutmeg, sugar, rum, and vanilla until smooth.

Pour the custard into a shallow casserole dish.

Place two slices of bread in the custard for about 30 seconds, flip, and soak for another 30 seconds.

Ensure slices absorb some custard without becoming soggy.

Transfer slices to the hot skillet or griddle and fry until golden brown and crisp, about 2 minutes per side.

Adjust heat as needed to avoid scorching.

Move cooked slices to the prepared baking sheet and place in the oven to keep warm.

Serve hot with butter and maple syrup, or dust with powdered sugar and add fresh fruit.