In a large pot or Dutch oven, heat the olive oil over medium heat. Once hot, add the diced onion and cook for about 5 minutes, or until translucent.
Add the minced garlic and sauté for an additional minute until fragrant.
Stir in the diced potatoes, corn kernels, vegetable broth, salt, black pepper, smoked paprika, and dried thyme. Bring the mixture to a boil.
Once boiling, reduce the heat to a simmer and let it cook for about 15 minutes, or until the potatoes are tender.
If you prefer a creamier texture, you can use a blender to puree a portion of the chowder and then stir it back into the pot, or you can crush some of the potatoes with a fork directly in the pot.
Pour in the milk and stir well. Allow the chowder to heat for an additional 2-3 minutes, then taste and adjust seasoning if necessary.
Serve hot, garnished with chopped parsley.