Preheat the grill to its highest setting.
Place the butter and sugar into a saucepan over a high heat and cook until melted.
Add the apples and cook for five to ten minutes, until caramelised and cooked through.
Heat a griddle pan until smoking and cook the slices of bread for one minute on each side. Cover with the blue cheese and place under the grill for 1-2 minutes, or until melted.
Spoon over the apples and the sprinkle with the dill to serve.