Preheat oven to 325℉ (160℃)
Combine eggs, yolks and sour cream in a small bowl and mix to combine. Set aside for use later.
2 Large Eggs, 2 Large Egg yolks, 1 Cup Sour Cream
Add sugar, flour, baking powder, cinnamon and baking soda in the bowl of a stand mixer fitted with the paddle attachment. Mix for one minute on low speed to combine ingredients. Note: a hand mixer may also be used.
2 Cups All-Purpose flour, 1 Cup Granulated Sugar, 1 teaspoon Baking Powder, 1 teaspoon Ground Cinnamon, 1 teaspoon Baking Soda
Add softened butter and mix on low speed for 3 minutes.
10 Tablespoons Unsalted butter
Add half of the egg/sour cream mixture to the mixing bowl and combine on low speed for one minute. Scrap down sides of bowl as needed.
Add remaining egg/sour cream mixture to the mixing bowl and combine on low speed for one minute. Scrape sides of bowl and mix on low speed for another minute.
Add the chopped apples to the cake batter. Stir in by hand until well distributed.
2 Medium Apples
Add ½ of the cake batter to the prepared pan and smooth with a rubber spatula. Use the back of a spoon to create a tunnel in the batter.
Pipe the cream cheese / dulce de leche mixture into the tunnel you just created. Take care to keep the mixture away from the sides of the pan.
Add the remaining cake batter to the pan. Smooth gently with an rubber spatula.
Bake for 50 minutes or until top is quite brown and a toothpick inserted in the center comes out clean.
Remove pan from oven and cool upright for 15 minutes.
Flip pan upside down onto a cooling rack and let cool completely with the pan still resting on the cake. Remove pan - cake should release from pan on its own. If not, use blunt knife and gently loosen sides.
After an hour, lift pan off of cake. Cake should release from pan own - if not, use a blunt knife to gently loosen sides.
Transfer cake to a serving platter.