Large data centers today already account for nearly 1.31% of total electricity consumption with cooling responsible for roughly 33% of that energy consumption. This energy intensive cooling problem is exacerbated by the presence of hotspots in multicore microprocessors due to excess coolant flow requirement for thermal management. Here we present a novel liquid-cooling concept, for targeted, energy efficient cooling of hotspots through passively optimized microchannel structures etched into the backside of a chip (embedded liquid cooling or ELC architecture). We adopt an experimentally validated and computationally efficient modeling approach to predict the performance of our hotspot-targeted ELC design. The design is optimized for exemplar non-uniform chip power maps using Response Surface Methodology (RSM). For industrially acceptable limits of approximately 0.4bar (40kPa) on pressure drop and one percent of total chip power on pumping power, the optimized designs are computationally evaluated against a base, standard ELC design with uniform channel widths and uniform flow distribution. For an average steady-state heat flux of 150W/cm2 in core areas (hotspots) and 20W/cm2 over remaining chip area (background), the optimized design reduces the maximum chip temperature non-uniformity by 61% to 3.7°C. For a higher average, steady-state hotspot heat flux of 300W/cm2, the maximum temperature non-uniformity is reduced by 54% to 8.7°C. It is shown that the base design requires a prohibitively high level of pumping power (about 2000 fold for 150W/cm2 case and 600 fold for 300W/cm2 case) to match the thermal performance of the optimized, hotspot-targeting designs. The pumping power requirement for optimized designs is only 0.23% and 0.17% of the total chip power for 150W/cm2 and 300W/cm2 hotspot heat flux respectively. Moreover, the optimized designs distribute the coolant flow without any external flow control devices and the performance is only marginally affected by the manifold geometry used to supply the coolant to the microchannel heat transfer structure. This also attests to the robustness of the optimized embedded microchannel structures.