Combine flour, butter, 1/2 cup sugar, and salt in a bowl. Add 3/4 of the white wine and mix into a smooth dough. Add more white wine as needed, but avoid making dough too soft. Shape into a ball, flatten, cover, and refrigerate for 30 minutes.
Peel apples and cut in half. Remove core and place into a bowl with cold water and lemon juice to prevent browning.
Preheat the oven to 375 degrees F (190 degrees C). Grease a rimmed baking sheet with butter and dust with flour.
Roll chilled dough out into a rectangle slightly larger than the baking sheet. Transfer dough to the baking sheet and press some of the dough up the rimmed sides to make an edge. Pierce all over with a fork.
Place apple halves cut-side down on a cutting board. Make several parallel cuts without cutting all the way through the apple. Arrange apples all over the dough. Sprinkle evenly with 3 tablespoons cinnamon sugar.
Bake in the preheated oven until apples start to lightly brown, 35 to 40 minutes.
Combine eggs, 1/2 cup sugar, vanilla sugar, and lemon zest in a bowl. Beat with an electric mixer until very foamy, 2 to 3 minutes.
Beat cream in a chilled glass or metal bowl with an electric mixer until stiff peaks form. Fold whipped cream into the egg mixture.
Remove cake from the oven and reduce temperature to 325 degrees F (165 degrees C). Pour egg-cream mixture over the apples and sprinkle with remaining 1 tablespoon cinnamon sugar.
Bake until cream topping is golden brown, 10 to 15 minutes.
