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Preheat the oven to 350°F Lightly grease (or line with parchment) two baking sheets.
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Beat together the shortening, sugars, egg, vanilla, and peanut butter until smooth.
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Add the flour, baking soda, and salt to the peanut-butter mixture, beating gently until everything is well combined. Add enough water to make a cohesive dough.
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Drop the cookie dough by tablepoonfuls onto the prepared baking sheets (a tablespoon cookie scoop works well here), leaving 2" between them.
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Use a fork to flatten each cookie to about 1/2" thick, making a cross-hatch design.
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Bake the cookies for 12 to 14 minutes, until they're barely beginning to brown around the edges; the tops won't have browned. Remove them from the oven, and cool on a rack.