Heat the olive oil in a large pot over medium heat. Add the onion and garlic and cook for 3 to 4 minutes until the onion softens.
Add the potatoes, broccoli florets, turmeric, vegetable broth, salt, and black pepper to the pot. Stir to combine.
Bring the mixture to a boil, then reduce the heat and simmer for 15 to 20 minutes until the potatoes are tender.
Remove the pot from the heat. Use an immersion blender to puree the soup until it reaches your preferred texture, leaving some small chunks if desired.
Stir in the chopped fresh parsley just before serving.