A method and assembly for preparing a drink based on frozen food comprises storing frozen food in various containers in the form of first granular materials and under deep- freeze conditions, crushing a portion of at least one of the first granular materials into a second granular material, and placing the second granular material into a cup. A first liquid is added to the cup at a temperature of at least 50° C. The cup, filled with the foods and possibly the first liquid, is closed, and the content of the cup is ground into a homogeneous mass. Lastly, the cup is opened and served.