Wash the potatoes and pat them dry. Spread sea salt in a fat pan, place potatoes on top and cook in the preheated oven (electric cooker: 200 °C/ gas: level 3) for about 30 minutes.
In the meantime, wash the basil, dab dry and pluck. Finely puree the basil and olive oil. Peel garlic and press it through the garlic press. Mix egg yolk and garlic and stir in the basil oil bit by bit.
Season with salt and cayenne pepper. Peel the asparagus to about 2/3 and cut off the woody ends. Roast the pine nuts in a hot pan until golden brown. Remove and put aside. Wash the tomato, dab dry and cut into quarters.
Remove seeds and stalk. Cut the fruit flesh into medium-sized cubes. Peel and finely dice the shallots. Mix pine nuts, tomato and shallots together. Take the potatoes out of the oven and peel the skin.
Keep potatoes warm. Wash lamb chops, dab dry and season with salt and pepper. Heat oil in a pan and fry the lamb chops in it for about 8 minutes on both sides. Meanwhile cook the asparagus in boiling salted water for about 8 minutes.
Arrange green asparagus with lamb chops, basil aioli and potatoes on plates. Put tomato salsa on the asparagus. Serve remaining basil aioli separately.