An apparatus for producing beverages. The apparatus comprises a dispensing system, a mixing unit, and a control unit comprising a user interface, which interact to prepare a particular beverage when requested by a user. When the control unit receives user input requesting the particular beverage via the user interface, it causes the dispensing system to dispense various ingredients (e.g., fragmented ice, water, flavoring ingredients, milk product) that are mixed by the mixing unit in order to prepare the particular beverage, which is served in a cup. In various embodiments, the apparatus may produce frozen beverages that include fragmented ice (e.g., shaved or crushed ice) as one of their ingredients, such as slush beverages and smoothie beverages, and/or hot beverages that include heated water as one of their ingredients, such as coffee and flavored coffee beverages (e.g., French Vanilla, Mocha, etc.).