How to make
Peel and chop the fresh garlic into pieces 0.6″ (1.5 cm) long. Wash the asparagus well under running water and break off the hard and stringy ends at the base.
Heat most of the olive oil over medium heat and fry the vegetables for 5-6 minutes. It is enough for the garlic to aquire a golden color and the asparagus to remain slightly crunchy. Season with salt and dried dill and set aside.
In a separate pan, heat the remaining olive oil over high heat (on the 8th degrees out of 9 or depending on your stove - one degree below the maximum). As soon as the olive oil starts to smoke lightly, sprinkle a little coarse salt and put the swordfish fillets in it. If the pan is big enough - all at once or if they don't fit, it is not a problem to cook them one by one, since they are quite large and the cooking time is short and there is no danger of the finished ones getting cold.
Sear each fillet for two minutes on each side if they are 1cm thick. If yours are thinner, sear them for a little less time, so that they don't dry out.
Arrange them on wide plates and garnish them with lemon slices, tomato slices (it is good to peel the tomato beforehand), the asparagus and garlic aioli. Sprinkle with coarse salt and freshly chopped parsley.
The fish is consumed warm with a glass of good white wine.
Enjoy your meal!