It isn't difficult to figure out how these popular molasses cookies got their name -- they are as big as lily pads!
In a large mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, ginger, soda, cloves, nutmeg, and allspice; beat until combined. Beat in molasses, water, and rum. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour. Divide dough in half. Cover and chill for at least 3 hours.
On a lightly floured surface, roll half of the dough at a time to about 1/4-inch thickness. Cut into circles with a floured 4-inch round cookie cutter. Place on a lightly greased cookie sheet. Bake in a 375 degree F oven for 9 to 11 minutes or until edges are firm and bottoms are just lightly browned. Cool on cookie sheet 1 minute. Remove; cool on a wire rack. Makes about 24 cookies.
Store cookies in airtight container at room temperature up to 3 days or in freezer up to 1 month.