Heat the olive oil in a large pot over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
Add the diced potatoes and vegetable broth to the pot. Bring to a boil, then reduce heat and simmer for about 10 minutes, or until the potatoes are tender.
Stir in the corn kernels, smoked paprika, and cayenne pepper (if using). Simmer for another 5 minutes.
Using an immersion blender, blend the chowder until smooth, leaving a few chunks of corn and potato for texture. If using a regular blender, be sure to let the chowder cool slightly before blending.
Stir in the heavy cream (or coconut milk) and season with salt and pepper to taste. Heat through for 2-3 minutes until warmed.
Remove from heat and ladle the chowder into bowls.
Garnish with fresh parsley before serving.
Notes
For a dairy-free version, substitute heavy cream with coconut milk.