Preheat oven to 350º F. Grease and flour a 9-inch cake pan, springform or square pan. (If you want to plate this, use a springform; otherwise, just serve it out of the pan.)
Peel and core the apples, then cut 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.
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.
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.
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).
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.
Cool in pan and serve. I doubt you'll have leftovers.
Recipe courtesy of Food52.