Preheat oven to 350F. Grease a ten-cup bundt pan.
Zest and squeeze the orange. Mix the juice with the milk and Cointreau. In a separate bowl, mix the flour and baking powder.
Rub the orange zest into the sugar.
Using a stand mixer, or an electric mixer, beat the butter and orange sugar until light and fluffy, about 3-4 minutes. Scrape the bottom and sides of the bowl.
With the mixer on medium speed, slowly drizzle in the oil.
Add the eggs, one egg at a time, waiting for each egg to completely incorporate before adding the next. Scrape the bottom and sides of the bowl.
Reduce speed to low, then add the flour mixture in three parts, alternating with the milk mixture, starting and ending with the dry ingredients.
Bake over the medium oven rack for 50-55 minutes, or until a toothpick comes out from the center of the cake with a few moist crumbs.
Remove from the oven, then immediately soak the cake with the now chilled syrup.
Allow the cake to cool in the pan for 25-30 minutes, then invert it over a wire rack or a serving plate.