Line an 8- x 4-inch loaf pan with plastic wrap, allowing 2 to 3 inches to extend over sides.
Combine espresso and rum in a shallow bowl. Brush or quickly dip one-third of ladyfingers (about 8) on both sides in espresso mixture, and place in bottom of prepared loaf pan.
Layer 1 cup ice cream over ladyfingers, and sprinkle evenly with one-third grated chocolate. Repeat 2 times with remaining ladyfingers, espresso mixture, ice cream, and grated chocolate.
Cover and freeze at least 3 hours or until ready to serve. Invert pan onto a serving platter, and remove pan and plastic wrap. Cut into 1 1/2- or 2-inch slices. Garnish, if desired.
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