Preheat oven to 180 degrees C (350 degrees F). Line a 18 - 20 cm baking tin with a circle of parchment paper.
Using a big sharp knife, chop the two kinds of chocolate into pieces (separately). You don’t need to make the pieces equal size.
In a bowl combine flour, cornstarch and baking powder and stir.
Melt the butter on a double boiler until only small pieces remain solid. Pour it into a large mixing bowl and whisk until completely melted. Add sugar and whisk energetically for 1-2 minutes. Add vanilla and eggs, one at a time, and whisk until almost smooth, scrapping out the sides.
Gradually add the dry ingredients, mixing gently with a wooden spoon until absorbed. At the end fold in the chopped dark chocolate.
Extend half of the dough onto the bottom of the prepared pan. Spread the chopped white chocolate on top. Cover with the rest of the dough.
Bake for about 40 minutes or until the edges of the cake start becoming golden brown. Let cool for 15 - 30 minutes before serving. You can serve it plain or garnish with ice cream or whipped cream.
Keep leftovers in airtight container. Reheat lightly before serving them so that the chocolate chunks melt inside.