In a large pot, melt the butter over medium heat. Add the diced onion and sauté until translucent, about 5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
Add the diced potatoes and corn to the pot, stirring to combine. Pour in the vegetable broth and bring to a boil. Reduce heat to a simmer and cook for 15-20 minutes, or until the potatoes are tender.
Using an immersion blender, blend the chowder until smooth, leaving some chunks for texture. If you don’t have an immersion blender, carefully transfer half of the chowder to a blender, blend until smooth, and return it to the pot.
Stir in the heavy cream, salt, black pepper, smoked paprika, and cayenne pepper (if using). Heat through for another 5 minutes, but do not let it boil.
Taste and adjust seasoning if necessary. Serve hot, garnished with sliced green onions and chopped parsley.