Preheat the Oven: Preheat your oven to 325°F (160°C). Ensure you have a 10-inch ungreased tube pan ready.

Mix the Dry Ingredients: In a large mixing bowl, sift together the all-purpose flour, cocoa powder, 3/4 cup of granulated sugar, baking powder, and salt.

Combine Wet Ingredients: In a separate bowl, whisk together the vegetable oil, egg yolks, warm water, and vanilla extract until smooth. Gradually add this mixture to the dry ingredients, stirring until well combined.

Whip the Egg Whites: In a clean, grease-free bowl, use an electric mixer to beat the egg whites with the cream of tartar until soft peaks form. Gradually add the remaining 3/4 cup of sugar while beating, and continue until stiff peaks form.

Incorporate the Egg Whites: Gently fold one-third of the whipped egg whites into the chocolate batter to lighten it. Then carefully fold in the remaining egg whites, being cautious not to deflate the mixture.

Bake the Cake: Pour the batter into the ungreased tube pan. Smooth the top with a spatula. Bake in the preheated oven for 55-60 minutes, or until a toothpick inserted in the center comes out clean.

Cool the Cake: Once baked, invert the tube pan onto a cooling rack and let the cake cool completely upside down.

Release and Serve: Once cooled, run a knife around the edges of the pan to release the cake. Slice and serve as is or with your favorite toppings.