Preheat the grill to its highest setting.
Soak the dulse seaweed in cold water for about 10 seconds, then drain well and roughly chop. Blend in a food processor until finely chopped, then add the softened butter and blend until well combined. Add the lemon juice and blend once more. (You can keep any you don't use in the freezer.)
To butterfly the mackerel, open up each mackerel belly and slide a sharp knife in under the rib cage, flicking the bones away from the flesh. Snip the bones at the head end and tail end, then lift out the whole rib cage and any bones. Open the mackerel out slightly, then spoon the butter down the centre, leaving just one large spoonful in the bowl.
Make 2 open parcels of aluminium foil to hold the mackerel and place them onto a baking tray. Lay the butterflied mackerel inside the foil parcels and grill for 5-10 minutes, until the butter has melted and the mackerel is just cooked through.
Meanwhile cook the vegetables. Bring 100ml/3½fl oz water to the boil in a large frying pan. Add the shallots and broad beans and simmer for 2 minutes, then add the peas and the pods and simmer for 1 minute. Add the asparagus spears and tarragon sprigs and return the water to a simmer. Add the last spoonful of dulse butter to the water and simmer the asparagus and vegetables for a further 2 minutes, or until the asparagus are tender and the butter has emulsified. Season the vegetables, to taste, with salt and freshly ground black pepper.
Lift the mackerel out of the aluminium trays and onto the serving plates, drizzling any excess butter from the trays over the top. Spoon the vegetables alongside.