Grease a 9x13-inch baking tray with a piece of butter and dust it with flour or breadcrumbs. To get rid of any excess flour, turn the baking tray onto a work surface and tap it gently.
Mix dry ingredients in a separate bowl: flour, cocoa, and baking powder.
In a mixing bowl, whisk the whole eggs in a bowl using an electric handheld mixer and beat them with the sugar on medium speed until a foamy mass is created. Gradually add the sugar as you increase the speed of the mixer. If the eggs are warmed to room temperature, and you are patient for 5 minutes or so, you will whip up a lovely fluffy foam. The wet mixture turns light in color while you whisk, the sugar will gradually dissolve, and the whole mass will thicken slightly.
Reduce the mixer speed to a minimum and gradually add the prepared dry flour mixture, milk, and oil to the beaten egg mass. Mix until everything is combined into a semi-liquid sponge cake batter with a light brown color.
Pour the batter onto the prepared baking sheet and smooth the surface.
Cook the chocolate pudding according to the manufacturer's instructions. I make pudding by heating the milk gently, whisking in the pudding powder and sugar, and bringing it to a boil over medium heat. I keep stirring so that no lumps form in the pudding.
Pour the hot pudding zigzag over the batter. Try not to let the pudding cover the surface in a uniform layer but leave gaps between the zigzags through which you can see the underlying batter.
Preheat the oven to 340°F/170°C (lower and upper heating). Put the coffee cake in the oven and bake for 30–40 minutes. The cake will puff up as it bakes. At the end of the baking time, test for doneness. Poke a skewer into the highest point to see if the cake is cooked. If the skewer comes out dry, you are done. If there is any batter residue on the skewer, let the cake bake for another 5 minutes and repeat the test with the skewer.
While the cake is baking, make the last cake layer of sour cream. Simply whisk the sour cream with sugar. When you take the cake out of the oven, immediately pour the sour cream on top and smooth the surface with a spoon or an offset spatula. It will become thinner with the heat and will spread well over the entire surface.
Allow to cool at room temperature. Finally, I recommend putting the cake in the fridge overnight. The sour cream will firm up and won't run when slicing the cake.