In a large skillet, heat the oil over medium heat. Add the onion. Cook for a few minutes, stirring occasionally, until the onions are softened. Add the garlic and sauté for another minute until fragrant.
Add the diced potatoes, vegetable broth, corn, coconut milk, nutritional yeast, salt, and pepper to the pot.
Stir well, bring to a boil over high heat, then reduce the heat and let it simmer for about 35 minutes, until the potatoes are tender and the corn can be easily chewed. Stir it every few minutes while simmering.
Use an immersion blender to blend about half of the chowder while leaving some chunks for texture. If the corn is not fully cooked, you'll notice pieces of the skin when you eat it - make sure it's fully cooked before blending.
Remove from heat, taste test and adjust the salt and pepper if needed.
If you're noticing pieces of corn skin even after blending, strain the soup through a large-hole colander, pressing out all the liquid except the corn skin.
Ladle the soup into bowls and garnish with fresh parsley. Serve warm with crusty bread or crackers on the side!