This study proposes a new thermofluid topology optimization (TO) framework to design an optimal liquid-based cooling plate for Li-ion battery packs. To resolve the numerical issues of the previous thermofluid TO formulation (i.e., intermediate densities and locally high temperatures), this study proposes new penalization schemes, i.e., black-and-white and temperature penalty schemes. In contrast to the previous scheme, the proposed schemes allow optimized materials to be clearly distinguished into solid or fluid phases. Additionally, they enable the suppression of locally high temperatures to achieve a uniform temperature distribution. To demonstrate the manufacturability of the prototype, an optimized cooling plate is manufactured. Experimental results validate the effectiveness of the proposed framework. The proposed optimization framework can be utilized to determine the optimal liquid-based cooling plate for EVs to achieve a low-pressure drop and a uniform temperature distribution.