Dry the bread
Cut the baguette into bite-sized pieces and spread them in a single layer on a rimmed baking sheet. Leave uncovered at room temperature for about 24 hours (or up to 48 hours) so the cubes firm up. If you’re short on time, toast them in a low oven until dry but not browned.

Make the cheesecake filling
In a bowl, beat the softened cream cheese with the 3 oz cream of coconut and ¼ cup sugar until the mixture is silky and lump-free. Transfer the mixture to a piping bag or a sturdy resealable bag and snip a corner for easier dispensing.

Whisk the custard
Whisk together the eggs, melted butter, 12 oz cream of coconut, milk, and ½ cup sugar until smooth and combined.

Assemble the bake
Grease a 9×13-inch casserole. Scatter half of the dried bread cubes across the pan. Pipe the cheesecake mixture over that first layer, distributing it in ribbons or dollops so most pieces get some coverage. Top with the remaining bread cubes, pressing gently to even things out.

Soak and top
Pour the egg-coconut custard slowly over the bread, pressing the cubes down so they absorb the liquid evenly. Sprinkle the shredded coconut evenly across the surface.

Bake
Bake at 375°F (190°C) for 45–50 minutes, until the edges are set and the center is just slightly wobbly. If the coconut or top browns too quickly, tent loosely with foil and continue baking until done.

Finish and serve
Let the casserole rest 10–15 minutes before slicing so it firms up a bit. Serve warm or at room temperature — a scoop of vanilla ice cream or a dusting of toasted coconut on top makes it extra special.