Combine the flour, baking powder, salt, and 1/2 cup of sugar in a bowl. Stir well to blend. Add the oil, egg yolks, coconut milk, and ube paste. Beat with an electric mixer until smooth.
Beat the egg whites and cream of tartar in a separate bowl until moist peaks formed. Gradually add 3/4 cup sugar, beating until stiff and shiny peaks are formed. Fold 1/3 of the egg whites into the egg yolks mixture, fold to mix and then add the rest of the egg whites. Fold gently but thoroughly, so no white streaks remain. Turn batter into ungreased 10" tube pan.
Bake for 60 mins or until a toothpick inserted in the center comes out clean. Invert cake and cool completely in pan. Make sure oven has reached 350°F before putting cake in oven. When cool, loosen the edges and shake pan to remove cake.
The nutrition information provided are only estimates based on an online nutritional calculator. This is not a comprehensive list of all the nutrients in the recipe (i.e., does not include vitamins, cholesterol, etc). I am not a certified nutritionist. Please consult a nutritionist or doctor for accurate information and any dietary restrictions and concerns you may have.