Preheat the oven to 350°F (175°C), with a rack in the center. Tear the croissants into bite-sized pieces and place them in a 1-quart (about 1-liter) baking dish. Set aside.
Combine sugar and water in a heavy bottomed saucepan, stir to dissolve the sugar, then put the saucepan on the stove. Cook on medium heat, without disturbing the pot, for about 10 minutes or until the sugar caramelizes. —> The mixture will bubble up as it cooks, going from a crystal clear color to a deep amber color.
Once it’s caramel in color, turn down heat to low and very slowly pour in the cream while whisking constantly. The mixture will splatter, so be careful and keep whisking. Once smooth, add the milk and rum. If you see any solid toffee keep whisking the mixture over low heat until the sugar melts.
Once completely smooth, remove mixture from the stove and whisk in eggs and zest. Pour custard over the croissants. Let sit for 10-20 minutes (the drier the croissants, the longer you should wait).
Bake for 20 minutes, until the custard is set. Let pudding cool for 10-15 minutes before serving. Serve as is or with a scoop of vanilla ice cream.