Heat olive oil in a large pot over medium heat. Sauté chopped onion for 5-7 minutes until translucent, then add minced garlic and dried thyme; sauté for another minute.
Pour in vegetable broth and add peeled, cubed potatoes. Bring to a boil, reduce heat, cover, and simmer for 15-20 minutes until tender.
Stir in broccoli florets, cover again, and simmer for another 5-7 minutes until bright green and tender-crisp.
Blend the soup until smooth and creamy using an immersion blender or by carefully transferring it to a countertop blender.
Return the blended soup to the pot; stir in plant-based milk, nutritional yeast, lemon juice, salt, and pepper. Heat gently without boiling.