You will need a 6-inch round cake pan with a removable bottom and a tall side and without any non-stick coating. Do not grease the pan at all. I do not recommend using a regular round pan lined with parchment paper on the bottom. I've tried this before and the base of the cake has a concave shape when I do this
Get the eggs out of the fridge and separate them when they are still cold. They are easier to separate when they are cold. Let the yolks and the whites come to a room temperature, this may take about 30 minutes or so
Prepare the filling: (can be done the day before)
Put cream cheese and sugar in a bowl and place this bowl over a pot with warm water and stir until cream cheese is softened and creamy. Put heavy cream in another mixing bowl and use a hand mixer to whip the cream over medium speed until just medium-soft peak. Do not whip until stiff. Add then fold in the cream cheese and Nutella (if using) until combined. Cover and keep it chilled in the fridge
Prepare cake batter:
Preheat your oven to 295 F (146 C) for conventional oven. If you have a convection oven, I suggest lowering the temperature by 20 F (15 C). Place the oven rack 2nd rack from the bottom (or adjust accordingly, you will know your oven best)
Place the egg whites in a clean mixing bowl. I use a stand mixer with a whisk attachment. You will have trouble whipping your meringue if there's a trace of grease in your utensils or bowls
In a separate bowl, whisk the egg yolks, milk, cream cheese, and oil. Sift the cake flour into the batter. Whisk to mix into a smooth batter. Set aside
Prepare the meringue:
Beat the egg whites on medium speed until frothy, add cream of tartar or lemon juice/vinegar and whip until it turns whitish and air bubbles are fine. Gradually add the sugar as you beat, in 3 batches. I beat them at medium speed (speed 6 on Kitchen Aid). This will take a bit longer compared to beating at high speed. I used to do higher speed (speed 8), but the meringue is smoother and nicer when I maintain the speed on 6 and much more stable too
I highly recommend stopping several times to check on the consistency and scraping the sides of the bowl to make sure no sugar left on the side of the bowl. Whip until you reach a stiff peak but still have a slight bent on the tip. Then lower the speed to 4 and whip for 1 minute to even out large bubbles and stop beating
Fold meringue into the cake batter:
Gently fold 1/3 of the meringue into the thick batter. Using a whisk, using a cutting motion and fold over to mix. Repeat this motion several rounds. Continue on with the second 1/3 of the meringue again to mix. For the last 1/3 of the meringue, use a rubber spatula instead to ensure you get all the batter at the bottom of the bowl mixed in as well. Use a cut down in the middle and fold over motion to fold gently but quickly. Make sure you don't see any more white meringue. The mixture should be fluffy and voluminous.
Pour the batter into the round cake pan. Use a rubber spatula to smooth the surface. Gently drop the cake pan from about 10 cm height on the counter 2-3 times. Use a skewer to draw a zig zag to pop bubbles inside the cake batter
Baking:
Put the pan on the positioned rack for 1 hour and then increase the temperature to 320 F (160 C) and bake for another 15 minutes or until the top is dry to touch and spring back lightly when you touch. The time is just for reference. Your oven may need less or more time to bake
Usually if you insert a skewer inside the cake and no crumbs stick to it or very minimal crumbs, it is safe to say that the cake is cooked through
Don't be alarmed if your cake has some cracks on top. What you are looking at will become the bottom of your cake. I know many people mind it a lot and make a big fuss when the top of the chiffon cake cracks, but actually it's not a flaw.
Cooling:
Drop the cake pan from about 10 cm height on the counter several times to prevent shrinkage when you pull the cake out of the oven. Then carefully invert the pan upside down immediately on a cooling rack. Please don't be tempted to remove it from the pan if it's still warm. It takes about one to two hours to cool down completely
Once it's cool down completely, use a spatula knife to run through the edge to help release the cake. Gently push the base to lift the cake out. Use the knife again to run through the base of the pan and then carefully release the cake.
Fill the cake:
Cut the cake into 4 large pieces (you can do 6 smaller pieces too if you prefer). Then cut each slice horizontally, taking care not to cut through into two slices. Fill each slice with the chilled cream cheese filling and then spread the filling on the cut side of the cake. Dip into milk powder on both sides of the chiffon cake. Repeat with the rest of the slice and arrange them back into a round cake for presentation. Dust with some milk powder on the surface of the cake. Top with some fresh fruit if you prefer.
Chill the finished cake:
Cover the cake and keep the cake chilled in the fridge for 24 hours if you can wait that long!