Moroccan mint tea is traditionally accompanied by hard cones or lumps of sugar. Sugar is central to the classic preparation, which combines green tea, spearmint, boiling water, and a generous sweetness.
Historically, sugar was often sold in large, dense cones or loaves rather than as the easily measured granulated sugar familiar today. A piece could be broken off and added to the teapot or served alongside the tea. This is why references to Moroccan tea may mention both sugar cones and sugar lumps.
The drink is commonly called atay or Maghrebi mint tea and is closely associated with hospitality. It is served throughout the day and offered to guests, often in several small glasses. Honey may appear in modern variations, but it is not the traditional accompaniment described by this question; butter and salt are unrelated distractors.