Heat the olive oil in a large pot over medium heat.
Add diced onion and cook until translucent, about 5 minutes.
Stir in minced garlic and cook for an additional minute until fragrant.
Incorporate the diced potato and stir for a couple of minutes.
Pour in the vegetable broth, add the chopped broccoli, and season with thyme, salt, and pepper.
Bring the mixture to a boil, then reduce heat and simmer for about 20 minutes.
Once the vegetables are tender, use an immersion blender to puree the soup until smooth.
Stir in the lemon juice and adjust seasoning if needed.
Serve hot, garnishing with extra olive oil or croutons if desired.