I got this out of a "Kyo no Ryori" magazine about 10 years ago, and make it every winter. You can make the same recipe as an upside-down cake too - Put the raw apple on the bottom, pour over the batter, and bake 20-25 mins at 180deg. C. But for dumplings...
3 large apples
up to 100 g sugar (roughly 1/2 a Japanese cup), raw (aka-zarame) or white.
2 tabs butter
2 tsp cinnamon
2 thin slices lemon
Peel and core apples, cut into 1/4s or 1/8ths and slice thinly.
Put all ingredients in a wide pan, add water just to cover and simmer covered about 5 minutes.
100g flour (1 scant Japanese cup)
2 tsp baking powder
4 tab sugar
2 tsp lemon juice
2 tab milk
1/2 tsp vanilla (US type), few drops vanilla oil or strong essence
2 tsp melted butter or oil
Sift dry ingredients together.
Stir egg, add sugar, beat thoroughly till pale and fluffy.
Add liquid ingredients alternating with sifted dry ingredients, adding butter/oil last.
Bring apple to a steady simmer, checking that apple is still covered by water and adding more if necessary. Drop tablespoonsful of batter into the simmering apple. Try not to let the dumplings touch each other.
Cover (For best results, put a cloth around the saucepan lid and use a peg or elastic band to gather very firmly over the top of the lid, so that there is no risk of the towel catching fire) and simmer 5-10 minutes until dumplings are risen and fluffy. 6-8 servings.