The present disclosure pertains to composite articles, and in particular a composite face plate for a golf club-head, and methods for making the same. In certain embodiments, a composite face plate for a club-head is formed with a cross-sectional profile having a varying thickness. The face plate comprises a lay-up of multiple, composite prepreg plies. At least a portion of the plies comprise a plurality of elongated prepreg strips arranged in a predetermined criss-cross pattern in the lay-up. The prepreg strips create one or more areas of increased thickness where the strips overlap each other, thereby creating a desired profile for the plate. Metallic or polymer covers or cover layers can be used to define a striking surface.