I want to cool down a lot of water with a huge ice cube. What's the best shape to maximize the rate of heat transfer?
The more surface area, the more heat transfer. Ideally you'd use a single-molecule sheet, but that's impractical. Practically, using crushed ice is very simple and very effective. You could also freeze water inside drinking straws or on baking sheets to achieve high area-to-volume ratios.
The size/shape of the container holding the liquid to be cooled has some bearing on the question. A thin sheet of ice has lots of surface area, but could interfere with convection bringing warm liquid in to mix with already-cooled liquid.
Whether this is relevant at all depends on factors like whether you're cooling a lot of liquid by only a degree or two, or cooling a small amount of liquid by a lot.
That is probably related to how much of the ice will melt in the process? (If hardly any ice will be left at thermal equilibrium, it won't take up much space, and probably didn't take long to melt most of it quickly.) Relative volume of the ice at the start and liquid at the start is a function of these things, but is another way of looking at them.
Will the mechanical action of adding the ice to the liquid cause significant currents?