Preheat your oven to 190°C (375°F). Halve the eggplants and remove the stems. Brush the cut sides with ghee and place them in the oven to roast for about 30 minutes.
After roasting, allow the eggplants to cool. Once cool, scoop out the flesh from the skin.
In a large pot, melt the butter over medium heat. Once melted, stir in the flour and cook for about 2 minutes, stirring continuously to avoid lumps.
Add the roasted eggplant flesh to the pot. Stir well to combine with the flour and butter mixture.
Gradually pour in the milk, mixing constantly to integrate it smoothly into the mixture.
Following the milk, slowly mix in the water to the pot, until it reaches your desired consistency.
Season the soup with salt. Bring the soup to a gentle simmer, stirring occasionally.
Use an immersion blender to blend the soup right in the pot, until it reaches a smooth consistency. Taste the soup and adjust the seasoning as needed. If you prefer an even smoother texture, you can strain the soup through a fine mesh sieve.
Finish the soup by stirring in some freshly ground black pepper for added flavor.
Serve the soup hot. For an extra touch, garnish each serving with a drizzle of chili butter and a sprinkle of chives.