Heat the oil in a large soup pot over medium-high heat. When hot add the carrots, celery, onion and garlic. Sauté until the vegetables just start to soften and the onion turns translucent and begins to brown, about 5 minutes.
Sprinkle the flour and thyme over the vegetables and stir to coat. Continue to stir and cook for about a minute until the flour starts to brown. Stir in the potatoes, vegetable broth, plant-based milk, and nutritional yeast. Bring to a simmer and cook until the potatoes are fork tender and the chowder has thickened, about 8 minutes.
Lastly, add in the corn and season with salt and pepper. If your chowder gets too thick, you can always thin it with water or a vegetable broth to the desired consistency. Serve hot.