Accurate monitoring and forecasting of vegetation health is essential for natural resource management, food security planning, and climate adaptation in water-stressed semi-arid environments. This study presents a comprehensive deep learning framework for forecasting the Enhanced Vegetation Index (EVI) across the four governorates of the Kurdistan Region of Iraq (KRI) --- Erbil, Duhok, Sulaymaniyah, and Halabja --- using a nine-year monthly record (January 2016 -- December 2024) derived from Sentinel-2 Level-2A Surface Reflectance imagery accessed via Google Earth Engine (GEE). Nine deep learning architectures spanning recurrent, hybrid convolutional-recurrent, and attention-based categories were trained and evaluated on a multivariate feature set comprising EVI, precipitation, air temperature, and cyclic month encoding. The Bidirectional Long Short-Term Memory (BiLSTM) model achieved the highest mean R² of 0.945 across all four governorates, with outstanding performance in Sulaymaniyah (R² = 0.977) and Halabja (R² = 0.964). Hybrid CNN-recurrent architectures, particularly CNN-BiLSTM-GRU, also demonstrated strong performance with the highest mean tolerance accuracy (0.985), confirming the complementarity of local convolutional feature extraction and temporal sequence modeling; however, BiLSTM remains the top-ranked model by R². By contrast, the standalone Transformer model performed poorly (mean R² = 0.132) due to the absence of positional encoding in the shallow single-block architecture. Predictive uncertainty was quantified using Monte Carlo Dropout inference, revealing well-calibrated epistemic uncertainty that peaks during the spring vegetation growing season. Autoregressive five-year EVI forecasts (2026--2030) and an exploratory ten-year projection (2026--2035) were generated by the BiLSTM model; forecasts commence in January 2026 as TerraClimate climate forcing data for 2025 were not yet publicly available at the time of analysis. Projected mean annual EVI values range from 0.145 to 0.194 across governorates, consistent with the historical climatological baseline. The 2022 regional drought anomaly is clearly captured in the historical record, confirming the sensitivity of the EVI signal to precipitation deficits. These results establish deep learning-based EVI forecasting as a viable and scalable tool for operational vegetation health monitoring in the KRI and comparable semi-arid dryland systems.