In this work, we present a type of compact binary diffractive optical element named Dual-Channel Radially-Coupled-Spiral Phase-Shift Zone Plate (DC-RCS-PZP) able to create two independent helico-conical vortex beams simultaneously. The proposed element makes it possible to individually control the topological charge, position, and effective handedness of the two beams in a unified optical aperture. The independent control of the two beams is achieved through the coherent addition of two non-separable radial- and azimuthal-phases belonging to the two channels. The parallel creation of two separate helico-conical beams with two independent vortex morphologies is demonstrated through both numerical and experimental results for the presented element. The two created beams display typical properties of helico-conical beams, including self-healing and radial- and azimuthal-flows of energy. The effectiveness of the proposed element makes it useful for realizing other applications involving the parallel and independent manipulation of structured optical beams in laser processing and optical communication applications such as simultaneous optical manipulation of two particles or parallel laser material processing and multiplexing of the orbital angular momentum.