Okay, these days they are called Refrigerator Cookies, but I'm betting that people didn't waste space in their ice boxes, those real ones that had the block of ice, on cookie dough. It's just that when this kind of cookie that you slice and bake some time after you put the dough together came out, people used the old name "ice box" to refer to that place to store cold foods.
Ice Box Spice Cookies
1/2 cup vegetable shortening
1/2 cup brown sugar
1 egg
1 tablespoon water
1 1/2 cups flour
1/4 teaspoon baking soda
1/4 teaspoon salt
1 1/2 teaspoons cinnamon
1 teaspoon nutmeg
1/2 teaspoon ground allspice
1/2 teaspoon ginger
(1/2 cup chopped nuts - sliced almonds would be nice)
Cream the shortening and sugar together until combined. Add the egg and water, and beat until light and fluffy. Combine the dry ingredients. Add to the first mixture, and beat until the dough is completely mixed. Stir in the nuts if you are using them. Shape the dough into a roll or rolls 1 1/2 inches in diameter (flour your hands and the work surface if you need to). Wrap in waxed paper or plastic wrap and chill until firm.
When ready to bake: Preheat the oven to 350 degrees and grease some cookie sheets. Use a thin, sharp knife to cut the dough into 1/3 inch thick rounds. Place about 1 inch apart on the cookie sheet and bake for about 10 minutes, until the cookies are lightly browned. Transfer to racks to cool.
From: The Fannie Farmer Baking Book, 1996
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I like refrigerator cookies for summer baking because you can freeze the dough and cook a few as you need them when the kitchen is cooler, like at night, or when a cold front comes through.