A supercritical carbon dioxide (sCO2) Brayton power cycle is considered as one of the promising energy conversion systems for a number of applications such as advanced nuclear reactors, advanced fossil, and Concentrated Solar Power (CSP) plants due to its high thermodynamic efficiency and small equipment size (heat exchangers and turbomachinery). The compact heat exchangers such as Printed Circuit Heat Exchangers (PCHEs) with micro-channel geometry are suitable for coupling different heat sources such as nuclear reactor to a sCO2 Brayton power cycle. PCHEs offer very high specific heat transfer area and pressure containment and are typically fabricated using chemical etching and diffusion bonding process [1]. Conventional semi-circular micro-channel PCHEs are used for recuperators and general use heat exchangers. The objective of this study is to design and optimize an advanced PCHE micro-channel geometry and topology for a sCO2 Brayton cycle. This work is concerned with the design where both sides of the plate are etched forming a double-etched micro-channel design configuration. In this advanced micro-channel topology, shim plates are needed to construct a PCHE stack using diffusion bonding. The design goals are to maximize heat transfer, minimize pressure drop, improve thermal performance and reduce the size, while maintaining mechanical integrity of a PCHE. Thermo-hydraulic performance of semi-circular micro-channel and advanced semi-circular and circular double-etched micro-channel geometries, i.e., the Nusselt number and Fanning Friction Factor (friction coefficient) and the overall heat transfer coefficient U between the hot and cold channels, pressure drop, and maximum stress, were determined and are reported in this work. The results obtained for the advanced double-etched microchannel geometry were compared to the "conventional" semi-circular single-etched (single-side etched) micro-channel design for the counter-flow arrangement. Using ANSYS-Workbench, a multi-objective optimization algorithm employing NSGA-II and Response Surface Approximation (RSA) as a surrogate model was used for design and optimization of the advanced double-etched micro-channel PCHE geometry. The channel fin, the channel pitch, and shim plate thickness were the parameters used in optimization. Alloys 617 and 230 were used as materials of construction.