Peel the potatoes if you prefer a smoother soup, or leave the skins on for added texture and fiber. Cut them into 1-inch cubes for quick, even cooking.
Dice the yellow onion into small, even pieces so they cook uniformly and release their sweet aroma when sautéed.
Heat the olive oil in a large pot over medium heat, until it shimmers slightly and you can hear a gentle sizzle when adding onions.
Add the diced onion to the hot oil and sauté for about 5 minutes, stirring occasionally, until it turns translucent and releases a sweet, fragrant aroma.
Stir in the cubed potatoes, coating them lightly with the onion and oil mixture, then pour in the vegetable broth and add a pinch of salt.
Bring the mixture to a boil, then reduce the heat to low, cover the pot, and let it simmer for 15-20 minutes, or until the potatoes are fork-tender and easily pierced.
Once the potatoes are soft, remove the pot from heat. Use an immersion blender directly in the pot to puree the soup until smooth, or transfer in batches to a blender and blend until creamy.
Stir in the nutritional yeast for added flavor and season with salt and pepper to taste. Blend again briefly to incorporate the seasonings evenly.
Taste the soup and adjust the salt and pepper as needed. If the soup feels too thick, add a splash of hot water or broth to loosen it up.
Serve the hot, silky soup in bowls, garnished with chopped green onions or fresh herbs for brightness and color.