Pat the mackerel dry with kitchen paper. Grill the mackerel, skin side up for 4-5 minutes under a hot grill. Season it with a little salt and leave to one side.
In a saucepan add the white wine and reduce to a tablespoon quantity. Take the pan off the heat, add the eggs and cream and then set to a low heat and gently stir. Add one cube of butter at a time and emulsify slowly. Once all the butter is combined add the lemon juice and salt to taste. It should be a slightly lumpy, but still loose, butter sauce.
Fry the garlic in a frying pan with a little oil and add the thyme, green beans and broccoli and cook until soft. Season with salt.
Place the vegetables on a plate, top with the mackerel fillet, then pour over the eggs and serve.