For the dressing, reserve around 12 of the most beautiful strawberries and mash the others with a little olive oil. Add the chopped puntarella and mix.
For the vegetables, blanch the beans in a small saucepan of boiling water for 2 minutes and then drain. When cool enough to handle, pop the beans out of their leathery skins by squeezing gently. Discard the skins.
For the fish, brush the skinless side of each fillet with beaten egg. Cover the same side with breadcrumbs.
Heat some oil and butter in a large frying pan with the garlic and thyme (you may need to use two pans). Fry the fish with the breaded side down. Cook for 6 minutes over a low heat. Season the fish with salt and pepper.
Meanwhile, heat some butter and oil in a large saucepan. Gently fry the shallots for 2 minutes then add the mousseron mushrooms and broad beans. Cook for 4 minutes over a medium heat. Season with salt and pepper.
To serve, divide the vegetables between serving plates, gently lay the fish on top, and add the dressing to the side. Garnish with the reserved strawberries and the cresses.