Extreme heat in hot-arid cities intensifies outdoor thermal stress, and neighborhood-scale conditions are strongly influenced by urban morphology. Although urban vegetation is widely promoted as a mitigation strategy, its cooling effectiveness under peak thermal stress remains poorly quantified and rarely integrated into a unified, decision-oriented metric. This study introduces the Vegetation Cooling Effectiveness Index (VCEI) as a unified framework to capture vegetation-driven cooling performance under extreme thermal conditions. Two residential districts in Aswan, Egypt, representing low-density and high-density urban fabrics, were investigated using a combined field measurement and microclimatic simulation approach. Continuous summer monitoring revealed extreme thermal exposure, with daytime air temperature (T-a) exceeding 44-45 degrees C and nighttime minima remaining above 28-30 degrees C; the high-density district exhibited persistently higher nocturnal temperatures by 1.0-1.5 degrees C, indicating enhanced heat retention. These observations were used to validate ENVI-met simulations of four vegetation scenarios relative to a vegetation-free baseline. Peak-hour analysis (12:00-16:00), representing the period of maximum daytime thermal stress, showed limited T-a reductions (<1.0 degrees C in the high-density district and <2.6 degrees C in the low-density district). At the same time, mean radiant temperature (T-mrt) reductions were substantial, reaching up to 11.4 degrees C and 15.9 degrees C, respectively. Corresponding physiologically equivalent temperature (PET) reductions ranged from 2.1 to 6.8 degrees C in the high-density district and 2.7 to 9.7 degrees C in the low-density district. When integrated through the proposed VCEI, spatially averaged effectiveness peaked at 0.57 under intermediate vegetation in the compact morphology, compared to 0.76 under dense vegetation in the open morphology, revealing clear density-dependent saturation effects. The results demonstrate that vegetation-based cooling under extreme heat is predominantly radiative and that optimal greening strategies must be tailored to urban density, highlighting the VCEI as a comparative evaluation framework for assessing vegetation cooling performance during peak thermal stress in hot-arid urban environments.