Peel and chop the potatoes into small, even pieces for quick and uniform cooking.
Heat the large pot over medium heat, then add a splash of water or oil and sauté the minced garlic until fragrant, about 1 minute.
Add the chopped potatoes to the pot and stir to coat them with the garlic aroma. Cook for 2-3 minutes.
Pour in the vegetable broth and add the thyme. Bring the mixture to a gentle boil, then reduce heat to low, cover, and simmer until the potatoes are tender, about 15-20 minutes.
Once the potatoes are soft when pierced with a fork, remove the pot from heat.
Use an immersion blender or transfer the soup in batches to a blender and blend until smooth and creamy. Be careful of the hot liquid!
Return the blended soup to the pot if using a blender, then stir in the plant-based milk. Heat gently until warmed through, about 3-5 minutes.
Season with salt and pepper to taste, then give it a final stir. The soup should be velvety, warm, and inviting.
Serve hot, garnished with a sprinkle of fresh herbs if desired, and enjoy the comforting flavors of this simple vegan potato soup.