Bake in preheated oven until pumpkin is soft and easily pierced with a fork, 30 to 40 minutes.
Scoop pumpkin flesh into a blender; add coconut water and blend until smooth, 1 to 2 minutes.
Pour pumpkin mixture into a saucepan and bring to a simmer over low heat; stir in butter, curry powder, ground ginger, chile powder, ground nutmeg, salt, and ground pepper. Thin soup with milk to reach desired consistency. Cook and stir soup until heated through, about 5 minutes.