In a large saucepan over medium heat, warm olive oil.
Add leeks and sauté until just slightly softened, about 3 minutes.
Add carrots, potato and ginger and sauté until the vegetables are just softened, about 5 minutes more.
Add stock, cover partially and simmer until the vegetables are completely softened, about 20 minutes.
Remove from heat.
In blender or food processor, puree soup in batches, leaving some texture, and return soup to pan.
Set pan over medium heat and stir in orange juice and zest. Season with salt and white pepper.
Ladle soup into warmed bowls and garnish each serving with an orange slice and a sprig of mint.
Serves 4 to 6.