If necessary, peel the asparagus at the bottom and cut into pieces.
Heat the butter or oil in a pan, fry the asparagus. Add the finely chopped garlic, season with salt and sugar.
When the asparagus is firm to the bite, stir in the quartered cocktail tomatoes. Heat the tomatoes only briefly, then deglaze the vegetables with vinegar. Season with freshly ground pepper and fresh chopped basil.