In a large bowl, mix together the vegetable oil, melted butter, egg, vanilla extract, salt, baking powder, and confectioners' sugar until smooth and creamy.
Mix in the all-purpose flour until a soft, cohesive dough forms.
Cover the bowl and refrigerate for at least 1 hour (or overnight). This step is essential for preventing spreading.
Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
Scoop 1 tablespoon of dough, roll into a 4-inch rope about 1/2 inch thick, then connect the ends to form a circle. Leave a hole in the center.
Place cookies 1 inch apart and bake for 16–18 minutes, or until set and lightly golden around the edges. Cool completely on a wire rack.
In two small bowls, combine 1/2 cup confectioners' sugar, 1 tablespoon milk, and 2 teaspoons light corn syrup each. Mix until smooth. Tint one bowl red and one green.
Dip or spoon the glaze onto the tops of the cooled cookies. Add sprinkles immediately before the icing sets.