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Preheat the oven to 350°F (180°C).
Grease and lightly flour a Bundt pan or loaf pan, making sure to coat all edges and ridges well.
Beat the eggs and sugar in a large bowl until pale and slightly fluffy, about 2–3 minutes.
Add the oil, milk, and vanilla. Mix until smooth.
In a separate bowl, whisk together the flour and baking powder.
Add the dry ingredients to the wet mixture and mix just until combined. Do not overmix.
Divide the batter evenly in half.
Stir the cocoa powder into one half of the batter until fully incorporated. If needed, add 1 tablespoon milk to loosen slightly.
For the marble pattern
Spoon half of the vanilla batter into the prepared pan and spread gently.
Drop spoonfuls of half of the chocolate batter over the vanilla layer.
Add the remaining vanilla batter, spreading lightly.
Finish with the remaining chocolate batter in scattered spoonfuls.
Insert a knife or skewer and make 2–3 gentle figure-eight motions to create the marble pattern. Do not overmix.
Bake for 35–40 minutes (short Bundt or loaf may take 40–50 minutes), or until a toothpick inserted near the center comes out clean.
Let the cake rest in the pan for 10–15 minutes, then invert onto a rack to cool completely.
Dust with powdered sugar before serving, if desired. Bon appétit.