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Step 1
Preheat the oven to 330 F. Lightly butter or oil an 8-inch square or round baking dish. If making multiple cakes, lightly butter or oil 5 to 6 (6-ounce) ramekins.
Step 2
Separate the eggs and place the yolks and whites in separate bowls.
Step 3
In a large bowl, whisk together the egg yolks, lemon juice, lemon zest, Greek yogurt, 1/2 cup sugar, melted butter, vanilla and salt. Sift or whisk in the flour and mix until smooth. Set aside.
Step 4
Using a handheld mixer or stand mixer with a whisk attachment, beat/whisk the egg whites on medium-high until soft foamy peaks form, about 1 to 2 minutes. Sprinkle in 1/4 cup of the remaining sugar and beat/whisk again until glossy peaks (to the touch) are formed, another 1 to 2 minutes.
Step 5
Fold half the egg whites into the egg yolk/lemon mixture. Gently stir to combine. Fold in the remaining egg whites and gently mix so a soft and airy but thick batter is formed.
Step 6
Transfer the batter to the prepared 8-inch baking dish or divide the batter evenly into 5 to 6 ramekins filling 3/4 full. Place the baking dish or ramekins in a deep pan or a large casserole dish. Create a water bath by gently adding hot water to the pan filling 1/3 to 1/2 way up the side of the ramekins or 1/2 way up the cake pan. Carefully transfer the pan into the oven and bake for 40 to 45 minutes for the 8-inch cake or 35 to 40 minutes for the ramekins. Check for doneness at 30 minutes.
Step 7
Remove the pan from the oven. Using oven mitts or a towel, carefully remove the cake pan or ramekins from the water bath in the baking dish. Place on a wire rack for 10 minutes before serving. (See notes)
Step 8
Serve warm or cool to room temperature and sprinkle with powdered sugar.
Step 9
Store leftovers in the refrigerator in an airtight container for up to 5 days. Reheat or let the cake come to room temperature before serving.