This work proposes a mathematical model and its validation for a solar cooker (SC) augmented with a tracking-type bottom parabolic reflector (TBPR) to evaluate its thermal behaviour in two configurations, without and with TBPR (denoted as SC1 and SC2, respectively). Energy, exergy, economic, and environmental (4E) analyses were performed to verify the techno-economic-environmental feasibility of the SC. The results show that SC2 achieved an explicit increment in the average instantaneous and overall utilization efficiency by about 32.69 and 13.3 %, respectively. Also, SC2 shows an enhancement in the daily energy and exergy efficiency by 27.27 and 30 %, respectively, over SC1. Results revealed that SC2 reduces the lifetime cost of cooking a meal than SC1, from 0.031 to 0.023 $/meal. Thus, it enables reduced money and energy payback time by 33.47 and 54.82 %, respectively, with a lower cost of exergy losses, according to the exergoeconomic parameter. Furthermore, using SC2 achieved high mitigation of total CO2 emission, with higher earned carbon credit (134.11 $) than SC1 by 64.74 %. Hence, the mathematical model reasonably predicts the performance of the cookers, SC1 and SC2, under different climatic and operational conditions. Also, the TBPR has a vital role in obtaining an economical, eco-friendly, and sustainable solar cooker.