In a large bowl, with a mixer on medium speed, beat molasses, oil, brown sugar, and egg until well blended.
In a medium bowl, mix 2 3/4 cups flour, salt, baking powder, cinnamon, ginger, and cloves. Stir into molasses mixture, then beat until well blended. Divide dough in half, gather each half into a ball, then flatten into a disk. Wrap each disk in plastic wrap and freeze until firm, about 1 hour.
Unwrap dough. On a lightly floured surface, with a floured rolling pin, roll one disk at a time to about 1/4 inch thick. With floured 3- to 4-inch cutters, cut out cookies. Place about 1 inch apart on buttered 12- by 15-inch baking sheets. Gather excess dough into a ball, reroll, and cut out remaining cookies.
Bake cookies in a 350° regular or convection oven until edges begin to brown slightly, 8 to 10 minutes; if baking two sheets at once in one oven, switch their positions halfway through baking. Let cookies cool on sheets for 5 minutes, then transfer to racks to cool completely. Pipe Powdered Sugar Icing over cookies as desired.
Powdered Sugar Icing: In a bowl, stir 2 cups powdered sugar, 1 1/2 tablespoons water, and 1/2 teaspoon vanilla until smooth. Tint to desired color by stirring in food coloring, a drop or two at a time. If icing is too thick to work with, stir in more water, a few drops at a time; if too thin, stir in more powdered sugar. Makes 2/3 cup.
Nutritional analysis per cookie.