To prepare base, place biscuits in your food processor and pulse until you have crumbs. In a mixing bowl, combine biscuit crumbs with cocoa powder. Add melted butter and mix well.

Line a 10-inch (25.5-cm) springform pan with parchment paper (cut circle to fit pan). Press crumbs evenly into bottom of pan.

Using a hand beater, mix cheese, sugar, and vanilla sugar. Wait two minutes and then beat again until sugar is completely dissolved and mixture is smooth. In a separate bowl, beat the eggs and add to the cheese mixture. Add sour cream, heavy cream, and cooled melted butter.

Separate one cup of cheese mixture and stir instant pudding mix into it. (Don’t skip this step, or the cake will be lumpy.) Return the mixture to the cheese filling and stir until smooth. Divide batter evenly into two bowls.

For the white batter, break white chocolate into pieces and place in a small bowl. Heat 1/2 cup heavy cream in a small saucepan and bring to a boil. Pour the cream onto the white chocolate in the bowl. Wait one minute and mix well. (If small bits of chocolate remain, melt mixture in microwave.) Mix until smooth. Combine with half of the cheese mixture and stir well.

Remove one cup of chocolate-cheese filling and stir in 1/2 package instant pudding mix. Return the mixture to the chocolate-cheese filling and stir well.

For the dark batter, break bittersweet and milk chocolate into pieces and place in a small bowl. Heat 1/2 cup heavy cream in a small saucepan and bring to a boil. Pour the cream onto the chocolate in the bowl. Wait one minute and mix well. Combine with the remaining bowl of cheese filling and stir until smooth.

Remove one cup of chocolate-cheese filling and stir in 1/2 package instant chocolate pudding mix. Return the mixture to the chocolate-cheese filling and stir well.

Transfer each batter into a bottle or pitcher with a spout. (A glass measuring cup will also do the trick.)

Place the springform pan on a cookie sheet to avoid spills. Pour a thin layer of the dark batter into the center of the pan, until it covers the crumb layer. Then pour a slow, narrow stream of white batter directly into the center of the dark batter until the dark batter forms a wide, dark ring. Repeat process, alternating dark and white batters, until both batters are finished. It’s important to keep the stream very slow and thin. If you pour quickly, the rings will merge, and your cake won’t have the concentric circle look.

Preheat oven to 350 degrees Fahenheit (180 degrees Celsius). Place a pan filled with water at the bottom of the oven to add moisture. Place the cake pan, still on the cookie sheet, in the oven and bake for one and a half hours until the edges are firm, but the center is still wet. Turn off oven. Open oven door and allow the cake to cool before removing. Refrigerate cake for 24 hours before serving (see note).

Slice cake using a long, sharp non-serrated knife dipped in boiling water. Wipe knife clean between each slice. First cut cake on the diameter, then in quarters. Cut three slices from each quarter.