Heat the oven to 375?F. Line a large rimmed baking sheet with aluminum foil.

Whisk the melted butter, 1/2 cup granulated sugar, and maple syrup together in a large bowl until a paste forms. Scrape onto the baking sheet and spread into an even layer.

In the now-empty bowl, whisk the eggs, dairy of choice, the remaining 1/4 cup granulated sugar, orange liqueur if using, vanilla extract, ground cinnamon, and kosher salt until fully combined.

Cut the loaf of bread crosswise into 3/4-inch to 1-inch-thick slices. Soak each slice until drenched but not falling apart, about 10 to 15 seconds per side. Place in a single layer on the baking sheet.

Bake until the tops are golden-brown and the sugar paste is bubbling, about 25 to 30 minutes. Remove from the oven, turn on the broiler, and flip the slices over.

Return to the oven and broil, rotating the pan halfway through, until bubbling and darkened slightly in color, about 2 to 4 minutes. Let cool slightly before serving.