Heat olive oil in a large pot over medium-high heat. Once hot, add chopped carrots, onions, and celery. Sauté for about 10 minutes until softened.
Stir in freshly minced ginger, garlic, paprika, cumin, nutmeg, and a pinch of cayenne pepper. Cook for an additional 2 minutes, letting the spices become fragrant.
Pour in 6 cups of vegetable broth, and season with salt and pepper to taste. Bring the mixture to a rolling boil, then reduce the heat to medium-low and cover. Allow the soup to simmer for approximately 20 minutes, or until the carrots are completely tender, stirring occasionally.
Remove the pot from heat and use an immersion blender to blend the soup until smooth. If needed, stir in up to 1 additional cup of broth to reach your desired consistency. Reheat gently if necessary.
To finish, stir in creamy coconut milk, a touch of honey, and a splash of lemon juice for a bright flavor. Alternatively, you can swirl the coconut milk into each bowl individually for a lovely presentation.
Serve the soup warm, and garnish with fresh parsley if desired.