Lightly grease a 9x13-inch glass baking dish with butter or nonstick spray.
In a small bowl, combine the raisins and rum.
Let sit for at least 1 hour at room temperature or cover and refrigerate overnight.
Slice the croissants in half lengthwise. Spread the softened butter on the cut side of the bottom halves and the ginger jam on the cut side of the top halves, then reassemble the croissants into sandwiches.
Cut each croissant sandwich in half crosswise. Arrange the pieces, cut sides up, in a snug single layer in the prepared baking dish.
Use a slotted spoon to lift the raisins from the rum, letting excess liquid drip back into the bowl. Scatter the raisins evenly over the croissants
In a large mixing bowl or blender, add the eggs, half-and-half, whole milk, sugar, vanilla extract, vanilla bean, cinnamon, and salt. You can also add the leftover rum from the raisin bowl, or omit it.
Whisk or blend until smooth and fully combined. For an extra silky custard, pour it through a fine-mesh sieve into a large measuring cup.
Slowly pour the custard evenly over the croissants, making sure all pieces are moistened.
Cover the dish and refrigerate for at least 1 hour or up to 8 hours (overnight). During the first hour, gently press the croissants down with the back of a spoon every 15 minutes to help them absorb the custard, but do not stir them around or break them up.
About 15 minutes before you're ready to bake, preheat the oven to 375°F.
Bake for 55 to 65 minutes, until the top is golden brown, the edges are set, and the custard is mostly set in the center with just a slight jiggle. A knife inserted near the center should come out mostly clean, with thickened custard but no liquid.
Transfer the dish to a wire rack and let cool for about 10 minutes before serving. Scoop or slice into portions and serve warm.