With the rack in the middle position, preheat the oven to 180 °C (350 °F). Generously brush a 2.5-litre (10-cup) bundt or tube cake pan with butter and dust with flour.
In a bowl, combine flour, baking powder, baking soda and salt. Set aside.
In another bowl, combine milk and sour cream. Set aside.
In a third bowl, cream butter, sugar and vanilla with an electric mixer. Add eggs, one at a time, and beat until smooth. At low speed, add dry ingredients alternately with the milk mixture.
In another bowl, combine cocoa powder and oil with a whisk. Add 500 ml (2 cups) of cake batter and combine.
Spread vanilla cake batter in the pan. Make a deep groove in the centre of the batter by spreading batter up the sides of the pan. Spoon chocolate batter in the groove. With a small spoon, gently swirl the two batters in small circular movements to create a marbled effect.
Bake for about 55 minutes or until a toothpick inserted in the centre of the cake comes out clean. Let cool for 10 minutes. Unmould cake, flipping on a wire rack. Let cool completely.
In a bowl, place chocolate. Set aside.
In a small saucepan or in the microwave oven, bring cream and corn syrup to a boil. Pour over chocolate. Let melt for 1 minute without stirring.
With a fork, stir until smooth. Let cool for about 5 minutes. Pour over cooled cake and let ganache fall over the sides.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.