Brewed beverage appliance and method

A beverage making appliance uses a specialized beverage container and a related method of brewing a beverage. The container includes a cup-shaped body having a floor, a circumferential wall, and a top opening, a filter element positioned above the floor, at least one aperture formed in the floor, and a cover releasably attached to the cup body and covering the top opening. The appliance includes a base adapted to receive a beverage receptacle, a reservoir, a housing, a brewing tray in mechanical communication with the housing and dimensioned to receive a container containing at least one drink ingredient having particles of a first size, a grinding mechanism and a water delivery mechanism to selectively deliver water from the reservoir to one of a brewed beverage outlet in fluid communication with the receptacle, and a hot-water outlet.