Preheat a griddle to 350°F to 375°F, or use a skillet over medium heat. Lightly coat it with nonstick cooking spray if needed.
In a large mixing bowl, whisk together eggs, eggnog, vanilla extract, cinnamon, nutmeg, and kosher salt until fully combined and smooth.
Dip one slice of brioche bread at a time into the eggnog mixture, ensuring both sides are coated. Let any excess mixture drip off back into the bowl.
Place the coated bread slices on the hot griddle and cook for 2-3 minutes per side, or until golden brown. Repeat with the remaining slices, adding more cooking spray to the griddle as necessary between batches.
Serve warm with maple syrup and a dollop of whipped cream.