Braised veg with apple

We have an apple glut at the moment.  My landlady's garden is home to a tall apple tree and this year the crop is tremendous.  Every morning there are windfalls on the lawn, and we're both hunting for ways to use them up. 
A lot of chutney has been made, and blackberry and apple jam - I'll post some recipes for those shortly - and apple cake.  And tonight I invented this.
It's a kind of spin on the classic way of cooking red cabbage, but with different cruciferae (because this was what I had in the fridge) and more apple than usual.  This would serve two as a main veg dish alongside something like vege-bangers, pan-fried halloumi or grilled fish.

2-3 windfall eating apples, cored but not peeled, and chopped
1/2 a head of broccoli, chopped
1/4 of a white cabbage, thinly sliced
2 cloves garlic, minced
1/4 pt vegetable stock
Paprika and black pepper

Cook the broccoli in the stock for 5 minutes, then add the chopped apples, cook for a couple more minutes and then add the cabbage, garlic and seasonings.  Stir frequently and cook until the apple has gone to a mush and the cabbage is cooked through.  Serve hot.