Looking for specific Apple Cake recipe

CINNOMIN was most likely used and maybe Nutmeg and Allspice. Combined with brown sugar or even white , this would account for the color of grandmas cake.  It's texture and from where she was from seems to lean towards a Bakva type dense, crumbly cake. Good luck in your search.

Did you use brown sugar or dark brown sugar? Grandma might have added a touch of molasiss to it this would also much darken color.. Glad it came out good  EDB

My Grand mother was from Boheima (a part of Poland) this was her mothers Apple cake receipe. She would be 115 years old so this is a old receipe.

350 degree oven for approx 80 minutes

Mix together:

4 cups cubed apples

2 cups sugar

1 1/2 cups oil (veg or blended)

2 tbs Cinnamon

Sift together

3 cups flour\1 tsp salt

1 tsp baking soda

2 tsp vanilla

mix dry and wet ingredients together

then  optional

1 cup walnuts

1 cup golden raisins

Bake in a tube pan that is well greased and floured

This cake will have a crunchy top and super moist inside

Enjoy

Actually there is acid, in the apples, and i believe in the molasses of the brown sugar.

I have a recipe that meets your description, but from a very american source from the 50s.  Are you sure it was a traditional Polish recipe?  If your grandmother ever cooked from american cookbooks or passed recipes with american friends,  it might not have been a traditional recipe from poland    If you want it, it's a wonderful recipe for applesauce cake, comes out brown and moist and wonderful.  Let me know and i;ll post it. 

I'm so surprised to read there's another person seeking a recipe like this. I looked e-ve-ry-where and tried out so many other applecake recipes, but this one is from Mary Berry, thé queen of baking from the UK. So, all credits to Mary Berry. I made only a few changes; I used pecan nuts instead of walnuts and I chopped the apples in small cubes. Since I don't remember which source I copied this recipe from, I'm adding it exactly as I copied it. The picture is mine, maybe it will stimulate your memory? Anyway, enjoy!

Apple Cinnamon cake Mary Berry

225 g soft butter 225 g light muscovado or light brown sugar 3 medium eggs 100 g walnut pieces, chopped 100 g sultanas 225 g self-raising flour 2 tsp baking powder 400 g cooking apples, peeled, cored and grated 1 tsp ground cinnamon light muscovado sugar for sprinkling extra chopped walnuts for sprinkling (optional) icing sugar for dusting (optional)

Preheat the oven to 180 degrees C. Lightly grease and base line a 9 inch (23 cm) deep round cake tin with greased greaseproof paper. Measure the margarine, sugar, eggs, chopped walnuts, sultanas, flour and baking powder into a large bowl and beat well for about 2 minutes until thoroughly blended. Spoon half the mixture into the prepared tin then spread the grated apple and ground cinnamon in an even layer on top. (I fancied a nice layer of apple so I thinly sliced the apple instead of grating it, but its down to personal preference) Spread the remaining cake mixture on top, level the surface then sprinkle generously with light muscovado sugar and walnuts. Bake in the pre-heated oven for about 1 1/4 – 1 1/2 hours or until the cake is well risen and golden brown (mine was cooked after 1 hour). Remove from the oven and leave to cool in the tin for a few minutes before turning out and leaving to cool completely on a wire rack. Dust with icing sugar to serve.

Nobody asked, but when has that ever stopped me? 

An old fashioned applesauce cake from the old betty crocker (yes, again) cookbook.  Guaranteed not to fail.    NIce dark brown, without using any brown sugar. 

APPLESAUCE CAKE

make 1 1/2 cups applesauce:

cut up

6 to 8 tart apples, add

1/4 cup water, cover and cook to a mush and sieve.   (I don't sieve, i just squash with the fork, and you can peel or not, as long as the pieces are not too big (if you don;t peel and don't sieve, just make sure the peel is no bigger than 1/2 inch - slice the apple vertically parallel to the core, then lay those pieces flat side down on your cutting board and chop across roughly, zap zap zap in one direction and zap in the other - a technique i learned from the galloping gourmet, whatever his name was)

Meanwhile, as they cook, grease and flour a 13 X 9 rectangular pan

preheat oven to 350 degrees

Cream together:

1/2 cups soft butter

2 cups white sugar (it comes out very dark, even with white sugar)

add and beat in:

1 large egg

stir in

1 1/2 cups of the above applesauce

Mix together:

2-1/2 cups all purpose flour

1-1/2 tsp soda

1-1/2 tsp salt

3/4 tsp cinnamon

1/2 tsp cloves

1/2 tsp allspice

add the dry mixture above alternately with

1/2 cup water

beginning and ending with the dry ingredients, stirring only enough to combine each time

stir in :

1/2 cups cut up walnuts (optional)

1 cup raisins (they call for seeded, cut up, but i always use regular)

bake for about 45 to 50 minutes till the top tests done (you can touch it lightly and it feels springy, a toothpick inserted in the center comes out clean or with just a couple of crumbs attached.