Heat a frying pan and toast the sesame seeds on a medium heat for about 3 mins.until golden brown. Cool on a plate.
Trim away the woody base (1-2 cm) of the asparagus. Heat the grill pan and grill the asparagus under just tender. Turn them regularly. Cut them into 3 cm pieces.
Squeeze 1 lime. Peel the ginger and grate the carrots using a fine grater. Combine the juice with the ginger, 2 tablespoons of olive oil and the soy sauce to create a smooth dressing. Season with salt and pepper.
Slice the tomatoes into strips. Cook the samphire in boiling water for about 3 minutes until just tender. Drain and rinse under cold running water to stop the cooking process. Thinly slice the basil and parsley.
Mix the asparagus with the sesame seeds, tomatoes, samphire and sliced herbs in a bowl. Pour over the dressing.
Heat the rest of the olive oil in a pan. Halve the mackerel fillets lengthwise. Fry for approx. 6 minutes. Turn them halfway.
Arrange the salad on 4 plates. Place the mackerel on top. Season with freshly ground pepper and serve with a slice of lime.
