Because the ice cream has to be softened and refrozen to assemble the cake, use a rich, creamy variety of ice cream with a high content of milkfat. Ben and Jerry’s, Häagen-Dazs, and Tillamook will all work soften and refreeze without sacrificing any creamy texture. Lighter ice creams, especially slow churn and low-calorie varieties are more likely to turn icy and unpleasant when refrozen.