Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Beat condensed milk, evaporated milk, white sugar, eggs, and vanilla extract together in a bowl until smooth. Add shortening, baking soda, cinnamon, salt, and ginger; beat until smooth. Stir flour and coconut into milk mixture until batter is smooth.
Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, about 40 minutes.