This is my mom's recipe for an apple cake I grew up with. I love the simple yellow cake and the way the apples get a little but soft, but still maintain their shape and flavor.
Kids can help out with the measuring and mixing, apple cutting if old enough, pushing the apples into the cake and of course sprinkling the powdered sugar! (M was a bit heavy-handed with the sugar, but it was still delicious!)
Sorry this is by weight, this is the German way of cooking, and officially the "best" way to bake as flour etc can settle and weight is more accurate. I have a little kitchen scale that I use.
1 stick butter (room temp and sliced)
3-5 apples depending on size, peeled, cored and cut into thirds or quarters. I like a mix of tart and sweet but any will do really. Use enough to push into the dough, but not overcrowd-see photo
150 grams sugar (2/3 cup)
2 large or 3 small eggs
200 grams sifted flour (roughly 1 3/4 cup flour I think...)
2 1/2 tspns baking powder
2-4 Tbspns milk
Preheat oven to 350. Cream butter and slowly add sugar. Add eggs one at a time and cream. Add sifted flour and baking powder and blend. Fold in cut walnuts if you want. Peel and cut apples into quarters. Score the tops of the apple slices about 2 mm deep- makes them look really pretty and cooks better. Add 2-4 Tbspns milk and mix until dough is thick but can pour into the cake form (thicker than pancake batter, but not a cookie dough.) Grease and flour a spring-form cake pan. Pour batter in, and spread it around. (It will seem like a very thin layer.) Push the apples into the dough in a pattern, about 1/2 way submerged. Put in oven for 40-50 minutes until cake is golden brown and toothpick comes out clean.
Cool on wire wrack and dust with powdered sugar (shake it through a sieve.) YUMMY!