Sweet omelet with fruit

Something like this omelet recipe was first published by Lady Forbes in 1910. The recipe said that instead of apples, you can add rhubarb, pitted plums or even blackberries to this food, I would also add pears.
Remove the core from the apples. Cut into slices of medium thickness. Pour 150 ml of water into a saucepan and cook the apples until soft. The main thing is not to digest. Remove from the heat, peel the apples and    and add butter, sugar and lemon juice. Mix everything thoroughly and cool it. Beat the eggs well with a whisk, as we usually do for an omelet. Pour them into the cooled apple mixture.
Grease a deep baking dish with butter and sprinkle with breadcrumbs. (Both the bottom and the walls). Pour the egg-apple mixture into the mold and sprinkle breadcrumbs on top too.
Bake in a hot oven for about half an hour, although in my oven everything turns out in 15 minutes. Before serving, turn the omelet onto a platter and sprinkle with powdered sugar. On top of the omelet, you can cover it with whipped cream and decorate with slices of apples or berries, if you serve it on a festive table.