This study presents a novel reflective unit-cell with wideband characteristics at millimeter-wave (mmWave) bands for application in Reconfigurable Intelligent Surfaces (RIS). The proposed unit-cell design demonstrates through full-wave simulations a superior bandwidth performance over the 26.50-29.45 GHz, targeting the n257 band of mmWave 5G. The design was created for dual-polarization operation, each controlled by a p-i-n diode to realise a 1-btt RIS. The design achieves impressive performance, maintaining a phase difference error within $\pm \mathbf{20}$ degrees across most of the 3 GHz bandwidth while reflecting over 80% of the energy. The increased reflectivity minimizes losses, while precise phase control improves beam pointing accuracy, crucial in low-complexity 1-bit systems. Numerical simulations also indicate that this unit-cell performs effectively in a 6-layer PCB stack-up. A comparison with state-of-the-art unit-cells for RIS design is also presented, demonstrating the advantages of the proposed design in terms of bandwidth, dual-polarization operation, and phase accuracy.