In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté for about 5 minutes until it becomes translucent.
Stir in the minced garlic and cook for an additional 1-2 minutes, being careful not to let it burn.
Add the cubed potato to the pot, followed by the vegetable broth. Bring the mixture to a boil, then reduce the heat and let it simmer for about 15 minutes, or until the potatoes are tender.
Once the potatoes are cooked, add the fresh spinach leaves to the pot. Cook for another 5 minutes until the spinach has wilted.
Remove the pot from the heat and use an immersion blender to blend the soup until smooth. Alternatively, carefully transfer the soup in batches to a blender and blend until creamy.
Stir in the plant-based milk, nutritional yeast, ground nutmeg, and season with salt and pepper to taste. If the soup is too thick, add a little more vegetable broth or water to reach your desired consistency.
Return the soup to the stove over low heat, warming it through before serving.