In a large bowl, beat oil, butter, eggs, vanilla extract, salt, baking powder, and powdered sugar until smooth. Add flour, beating until smooth. Cover bowl with plastic wrap and place in the refrigerator to chill for at least one hour.
Preheat oven to 350 degrees F. Line two baking sheets with parchment paper.
Scoop the dough into 2 teaspoon-sized balls. Roll the balls into ropes about 4-inches long and about 1/2-inche diameter. Coil the ropes into round doughnut shapes, leaving a small hole in the middle.
Place the cookies on the prepared baking sheets about 1-inch apart. Place in the oven and bake for approximately 18 minutes or until the cookies have just a slight golden color on top, but will not be brown. Remove from the oven and transfer to a rack and cool completely before icing.
When cookies are cooled, dip the top of each cookie in one of the icings and place back on rack to let the icing harden completely.
Makes approximately 42 cookies.
2 cup powdered (confectioners') sugar, divided
4 teaspoons milk, divided
4 teaspoons light corn syrup, divided
Your choice of food coloring
Place 1/4 cup powdered sugar into four (4) tiny bowls. Add 1 teaspoon milk and 1 teaspoon corn syrup to each bowl. Stir together until you have made a spreadable icing. Add additional milk, drop by drop, until you reach the desired consistency.
Tint the icing in each bowl a different color.