Whisk the eggs, 1/4 cup sugar, the milk, orange zest, orange juice and vanilla in a large bowl. Put the croissants in an 8-inch-square baking dish, squeezing them in to fit in a single layer. Pour the egg mixture over the croissants, then put a plate on top and press down to keep them submerged. Let soak in the refrigerator, at least 30 minutes and up to 1 hour.
Preheat the oven to 350 degrees F. Remove the plate from the croissants, cover the baking dish with aluminum foil and bake until set, about 40 minutes. Remove from the oven and turn on the broiler. Uncover the baking dish, sprinkle with the remaining 1 tablespoon sugar and broil until the sugar is bubbling in spots, about 2 minutes.
Meanwhile, mix the marmalade with 1/4 cup water in a small microwave-safe bowl; microwave until warm, 1 to 2 minutes. Serve on the side.