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Step 1
Preheat oven to 325°F (163°C). Grease the inside of a 7 inch round cake pan with a cooking oil spray. Use a solid one-piece cake pan (no removable bottom). Line with parchment paper. You will want to create handles first and then line the bottom and sides. See notes for how to line the cake pan.
Step 2
Separate egg yolks and whites. Place eggs whites into fridge until ready to use. Let the egg yolks sit out.
Step 3
Add chocolate chips to a large microwave safe mixing bowl. Melt either in the microwave or on the stove (using the double boiler method). I used the microwave. If using microwave, heat chocolate in 15 second intervals, stirring in between with a spatula, until chocolate is completely melted and smooth.
Step 4
Whisk in yogurt. Make sure your yogurt is not cold to the touch before adding it. If bringing it to room temperature is not enough, you can warm up the yogurt for a few seconds in the microwave. If your yogurt is cold it will make your chocolate seize. Mix in the yogurt with a whisk until fully incorporated and the batter is smooth.
Step 5
Whisk in egg yolks until batter is smooth and no egg streaks remain.
Step 6
Remove egg whites from fridge. Place them into a separate clean large mixing bowl. Beat at highest speed until stiff peaks form. I prefer to use a stand mixer but you can also use a hand mixer.
Step 7
Add one third of the egg white mixture to your egg yolk batter. Fold it in gently with a spatula until no egg white lumps remain (it's okay if there are a few streaks of white in your batter). Make sure you scoop up batter from the very bottom of the bowl each time you fold to make sure all of the batter gets incorporated with the egg whites. Repeat with the next 1/3 and then remaining 1/3.
Step 8
Pour batter into prepared baking pan. The cake will be baked in a water bath. To do this, place your cake pan into a slightly larger baking pan. I used a 9 x 9 inch baking pan. Place your cake pan into the bigger pan. Pour just enough cold tap water into the outer pan so that the water level reaches 1/2 inch. Make sure to add the water to the outer pan after you've put the cake in. If you add 1/2 inch of water before, the added weight of the cake pan and cake batter will push up your water level more than 1/2 inch. I recommend using a ruler to measure the water level. If your water level is too high, the bottom of your cake will cook too much, causing a dense bottom layer.
Step 9
Place cake with water bath into your oven. Bake for 40-45 minutes or until cake looks done. (Check on the cake through the oven window and don't open the oven door. You just want the top of the cake to look cooked.) Turn off the oven but do not open the oven door and leave the cake in the oven for one hour. It is important to leave the cake in the oven (unopened) because this allows the cake to finish cooking and the gradual drop in temperature prevents the cake from suddenly collapsing. The cake will shrink down, but it shouldn't completely collapse. After one hour, you can remove the cake from the oven. Use the cake handles to lift the cake from the pan and transfer it to a plate. Let the cake cool to room temperature for a few hours. If desired, dust top with powdered sugar before serving.