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1
Preheat oven to 350u00b0 F. Grease and flour a 9-inch round cake pan or springform, or an 8X8-inch square pan. (If you want to plate this, use a springform; otherwise, just serve it out of the pan.)
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2
Peel and core the apples, then cut each apple into ~12 slices. Sprinkle with lemon juice (you don't need much - maybe a tablespoon or so for 4 apples) while the others are being sliced to prevent browning.
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3
Heat margarine in pan over low heat and add apples and 1-2 T white sugar. Stir for ~10-15 minutes until apples soften. Some of the liquid will soak into the apples, but if too much of it starts to evaporate, then turn the heat down.
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4
While the apples are on the stove top, mix together the remaining ingredients (except for the demerara sugar) -- flour, sugar (the 3/4 C), eggs, oil, baking powder, and vanilla. No mixer is required - you can just mix everything by hand even though the batter is quite thick.
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5
Add half the warm apples (juices and all) to the batter and mix. Then pour into the prepared pan and spread the batter evenly with a spatula . Arrange the remaining apple slices on the top of the batter as decoratively as possible (though even a mishmash will look nice).
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6
Sprinkle the cake with demerara sugar if you'd like and bake for 1 hour. As it bakes, the high egg content causes the cake to rise up as the heavier fruit sinks slightly and the demerara sugar helps creates a crackly crunchy crust that caramelizes slightly at the edges and where the fruit juices pool.
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7
Cool in pan and serve. I doubt you'll have leftovers.
