Ethiopia has experienced rapid electric vehicle (EV) adoption following the 2024 ban on fossil fuel-powered vehicle imports, with over 140,000 EVs now operating in Addis Ababa. However, charging infrastructure remains severely inadequate, with only a handful of stations currently serving the city. This study develops an optimized EV charging station network model for Addis Ababa using a network optimization approach. The optimization model, implemented in anyLogistix, considers geographic distribution of EV demand, existing and planned station locations, capacity constraints, cost minimization, and service coverage objectives. The model identifies 1,176 optimal station locations comprising 168 super-fast charging hubs (150 kW), 462 medium-power stations (50 kW), and 546 residential charging points (22 kW) — matching the Ethiopian government's stated infrastructure requirement. The optimized network achieves 94.2% coverage of EV users within a 5-kilometer radius at a total infrastructure cost of $258.4 million, representing a 75.8-percentage point improvement in coverage over the current baseline of 18.4%. Sensitivity analysis reveals that EV adoption rate and coverage radius are the most critical parameters affecting network performance, with ±20% variation in EV adoption resulting in ±$51.7 million change in total cost. The findings provide practical guidance for policymakers and utility providers in Ethiopia's ongoing infrastructure expansion and contribute to the emerging literature on electric mobility infrastructure planning in developing country contexts.