Peel the potatoes and cut them into uniform chunks about 2 cm (0.8 inch) thick. This helps them cook evenly and mash smoothly.
Finely dice the onion and mince the garlic, preparing them for sautéing.
Heat the neutral oil or vegan butter in a large heavy-bottomed pot over medium heat until it shimmers and starts to smell fragrant.
Add the diced onion to the pot and sauté, stirring frequently, until it becomes translucent and fragrant, about 5 minutes. You should see it soften and turn a gentle golden color.
Stir in the minced garlic and cook for another minute until it releases a warm aroma, being careful not to let it burn.
Add the potato chunks to the pot, stirring them with the onion and garlic. Sauté for 2-3 minutes until they start to soften and absorb the flavors.
Pour in the vegetable broth, bringing the mixture to a gentle simmer. Add the sprig of thyme or rosemary if using, and reduce the heat to low. Cover the pot partially and cook for about 20 minutes, until the potatoes are tender and easily mashable.
Remove the herb sprig if used, then use an immersion blender directly in the pot or carefully transfer the soup to a blender. Puree until smooth and velvety, with a few small potato bits for texture if desired.
Return the blended soup to the low heat, stirring well. Season with salt and pepper to taste, and add a squeeze of lemon juice or vinegar if you like a bright finish. Let it sit for a couple of minutes to meld the flavors.
Serve the soup hot, garnished with a drizzle of olive oil or fresh herbs if desired. Enjoy the velvety, comforting bowl of pantry-inspired vegan potato soup.
