Melt the butter in a frying pan, add the sugar and stir over a low heat until the sugar has dissolved.
Add the apples to the pan and cook for 3–4 minutes on each side until they start to caramelize, then stir in the walnuts and cook for 1 minute. Remove from the heat and leave to cool.
Place the red cabbage and celery in a bowl, then add the cooled apple and walnut mixture.
Make the dressing. Place the oils and vinegar in a screw-top jar with salt and pepper to taste, add the lid and shake well.
Drizzle the dressing over the ingredients in the bowl and toss together. Serve immediately, scattered with the blue cheese.