An ice making assembly and method utilizes a housing having an upper fluid chamber, a plurality of distinct, substantially vertical fluid channels, and at least one drain aperture in fluid communication with a fluid reservoir. Ice forming members extend from an ice forming evaporator into respective fluid channels. During an ice making event, fluid continuously supplied to the upper fluid chamber flows into each of the fluid channels and out through at least one drain aperture into a fluid reservoir below. The ice forming members are cooled such that fluid flowing across the fluid channels freezes on the ice forming members over time, forming clear ice pieces. The ice pieces are subsequently released from the ice forming members and transferred for storage and/or dispensing.