Preheat oven to 350°F.
In a large bowl, combine the oil, butter, molasses, brown sugar, egg and vanilla. Stir until well blended and smooth.
In a medium bowl, stir together the flour, baking soda, cinnamon, ginger, allspice and salt; add to the molasses mixture and stir by hand just until you have a soft dough.
Roll dough into 1"–1 1/2" balls and roll the balls in sugar to coat. Place about 2" apart on a cookie sheet that has been sprayed with nonstick spray.
Bake for 12–14 minutes, until just set around the edges. Transfer to a wire rack to cool or serve warm. Store extras in an airtight container or freeze. Makes 20 cookies.