Preheat your oven to 325°F and grease and flour an 8-inch round cake pan.
In a large bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, beat eggs and sugar with an electric mixer on medium speed until fluffy, about 2 minutes.
Add 1/2 cup milk, vegetable oil, and vanilla extract to the egg mixture. Mix until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Divide the batter evenly into two bowls.
Mix cocoa powder with 1/4 cup milk to form a paste. Stir the paste into one bowl of batter to make it chocolate.
Start by adding 1/4 cup of vanilla batter to the center of the prepared pan. Next, spoon 1/4 cup of chocolate batter on top of the vanilla layer. Keep alternating the batters, always pouring into the center, until you have used all the batter.
Place in the preheated oven and bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes. Then, remove it from the pan and let it cool completely on a wire rack.