Sauté the aromatics: Warm the olive oil in a large pot over medium heat. Add onion, celery, and carrot.
Cook for 5–6 minutes, stirring, until softened and lightly translucent.
Add garlic and spices: Stir in garlic, thyme, smoked paprika, and the bay leaf. Cook for 30–60 seconds until fragrant. Don’t let the garlic brown.
Add potatoes and broth: Stir in the diced potatoes and pour in the vegetable broth. Bring to a gentle boil, then reduce to a simmer.
Cover and cook for 10–12 minutes, until the potatoes are just fork-tender.
Add the corn: Stir in the corn kernels. If using frozen corn, no need to thaw first. Simmer uncovered for 5 minutes to heat through and let flavors mingle.
Make it creamy: Pour in the coconut milk and add the nutritional yeast, if using.
Simmer for 2–3 minutes. Taste and season with salt and pepper.
Thicken the chowder: For a classic chowder texture, use an immersion blender to blend about 1/3 of the soup right in the pot, or transfer a couple of ladles to a blender and purée until smooth. Return to the pot and stir.
The soup should become creamy but still chunky.
Brighten it up: Remove the bay leaf. Stir in lemon juice or apple cider vinegar to lift the flavors. Adjust salt and pepper as needed.
Garnish and serve: Ladle into bowls and top with chopped parsley or chives.
Add a crack of black pepper or a pinch of smoked paprika for color.