Integrating thermal energy storage (TES) for solar systems is crucial for better performance. To ensure the completion of solar cooking activity under fluctuating solar irradiance and reduce the subsequent loss, the integration of thermal storage to a solar cooker can play a vital role. Thus, this paper reveals the thermal performance of a solar cooker with a tracking type bottom parabolic reflector (TBPR) retrofitted with a new design of absorber plate integrated with thermal storage. Paraffin wax, a phase change material, acts as thermal storage. The TES integrated cooker is tested in two configurations, i.e., without TBPR (SC1) and with TBPR (SC2), to assess the impact of a design change on the thermal performance parameter (TPP) under field conditions. The cooker opto-thermal ratio (COR) and the first figure of merit (F1) acts as TPPs. The Levelized cost of the cooking a meal (LCCM) enables the economic analysis of the cooker. The average values of COR for cooker SC1 and SC2 are 0.118 and 0.140 (m2⋅K)/W, respectively. The cookers SC1 and SC2 attain the reference cooking temperature in ~75–82 min and ~61–66 min, respectively, and retain the heat at temperatures ~70–72 ◦C until 18:00 h in the evening. The LCCM for the cookers SC1 and SC2 are approximately the same ~0.024 ± 0.0005 USD/Ml. Nevertheless, SC2 exhibits additional advantages like increasing the cooked meals in the year and extending cooking periods (early morning and late afternoon cooking). Thus, the present work provides useful insights on TPP based rating/grading of the proposed solar cooker with thermal storage and its connection with the solar cooker economics in terms of LCCM.