In a large pot, heat the olive oil over medium heat. Add the diced onion and cook for about 5 minutes until softened. Stir in the minced garlic and cook for another minute until fragrant.
Add the diced potatoes to the pot and pour in the vegetable broth. Bring the mixture to a boil, then reduce the heat and let it simmer for about 15 minutes, or until the potatoes are tender.
Stir in the corn, dried thyme, smoked paprika, salt, and pepper. Let it simmer for another 5 minutes to allow the flavors to meld.
Using an immersion blender, blend a portion of the chowder to create a creamy texture while still retaining some chunky pieces. If you don't have an immersion blender, carefully transfer about half of the soup to a blender, blend until smooth, and then return it to the pot.
Stir in the coconut milk and heat the chowder gently until warmed through. Adjust seasoning with more salt and pepper if needed.
Ladle the chowder into bowls and garnish with chopped parsley or chives.
Notes
For a spicier version, add a pinch of cayenne pepper.