A note about the measurements: If you aren't in North America, 1 U.S. cup is 220ml. Remember that all the ingredients here are proportional, and can be scaled proportionately up or down.
4 to 5 medium or small apples - about 4 cups worth of cut up apple, but you can do it with a bit more or less
1 1/2 cups all-purpose flour
1/2 cup granulated sugar
2 tsp. baking powder
1/2 tsp. salt
1/2 cup whole milk
1 'large' egg, beaten
1/3 cup melted butter, or a combination of melted butter and neutral-tasting oil such as safflour or canola
For the crumble mixture:
3/4 cup of raw cane sugar, muscovado sugar, or regular light brown sugar
1/4 cup all-purpose flour
2 Tbs. butter
1 tsp. cinnamon (optional)
Preheat the oven to 180° C / 350° F.
Grease a standard square cake pan (20cm x 20cm x 5cm, or 8" x 8" x 2") with butter.
Sift the flour and baking powder together, and mix in the granulated sugar. Add the milk, beaten egg and melted butter or butter/oil combo; mix together just until there are no huge lumps. Pour into the pan.
Make the crumble mixture: melt the butter in a pan, add the flour, sugar and cinnamon, and mix well until it become crumble.
Peel, core and cut up the apples, and put on to of the cake batter. Sprinkle the top with the crumble mixture.
Bake for about 40 minutes. Cut into squares. Serve warm plain or with whipped cream. You can nuke this to warm it up quite successfully. Also nice at room temperature, such as in a lunch box.
OP had the sub headline as "dairy free" so I don't think a recipe with a lot of cow milk and butter would work.