Preheat the oven to 220 °C. Bring plenty of water to the boil in a sauce pan. Notch the tomatoes crosswise at the bottom. Prick them on a fork and plunge them into the boiling water for 10-12 seconds.
Skin the tomatoes. Cut the tomatoes into quarters. Remove the seeds and cut the flesh into tiny 2-3 mm cubes.
Toast the pine nuts in a dry frying pan until golden brown and shake them on a plate. Place the gratins on the baking tray and bake in the preheated oven for 20-25 minutes until golden brown and cooked through.
Heat the grill pan. Cut off the woody end and brush the asparagus thinly with 2 tablespoons of olive oil. Grill the asparagus in 2 portions for 5-6 minutes until al dente. Place them on a platter.
Meanwhile, boil the tarragon vinegar with the shallot and peppercorns until reduced by half. Melt the butter on low heat in a sauce pan without colouring it. Remove the melted butter from the heat.
Heat the remaining olive oil in a frying pan. Fry the onion and garlic for 3 minutes without colouring. Stir in the capers, olives, tomato and parsley. Keep the antiboise warm on low heat.
Place the egg and yolk with the tarragon leaves in a measuring cup. Pour the vinegar mixture through a sieve into the measuring jug. Slowly pour in the melted butter and whisk with the hand blender to make a creamy sauce. Season the bearnaise sauce with salt and pepper.
Place the gratins on 4 plates. Spoon the antiboise on and around the gratins. Top with the grilled asparagus and parma ham. Serve with the bearnaise sauce.
