Heat your oven to 180°C/Fan 160°C/Gas 4. Finely grate ½ the chunk of Parmesan into a bowl. Grate in the lemon zest. Throw in ½ the breadcrumbs and most of the thyme leaves. Season well with salt and pepper. Pour in 1 tbsp olive oil and mix.
Scrub the potatoes and chop into equal sized chunks. Place in a pan and cover with salted boiling water. Bring to a boil, then simmer for 10 mins till nearly cooked through.
While the potatoes simmer, trim the French beans. Halve them. Add them to the potatoes after they have simmered for 10 mins. Cook for 2 mins. Drain the potatoes and beans, then leave to dry in the colander.
Place the hake fillets on a baking tray lined with baking paper, skin-side down. Spoon the parmesan and herb crust over the top of them and press it down. Bake for 10-12 mins till the fish is cooked through (white and flaky) and the crust is golden.
While the fish cooks, peel and thinly slice the garlic. Place the pan you used to cook the potatoes back on the heat. Pour in 1 tbsp oil. Add the garlic, potatoes and beans. Cook for 5 mins to warm everything through, stirring now and then. Squeeze in juice from half the lemon and add plenty of salt and pepper.
Pop the hake on two warm plates. Pile on the garlicky beans and potatoes. Serve with a handful of peppery salad leaves and scatter over the last of the thyme leaves to serve.