Herby root vegetable gratin

Name: Herby root vegetable gratin
Ingredients: 25g butter plus extra for greasing; 1 onion thinly sliced; 425ml double cream; 300ml milk; 1kg potato thinly sliced; 350g swede thinly sliced; 350g parsnip thinly sliced; small bunch parsley; 2 tbsp thyme leaf; 1 garlic clove crushed; 50g parmesan (or vegetarian alternative), grated; 3 tbsp olive oil