In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until softened, about 8 minutes. Stir in half a teaspoon of salt along with the minced garlic and cook for another minute until fragrant.
Pour in the vegetable broth and bring the mixture to a boil.
Stir in the potato chunks, chopped parsley, freshly ground pepper, and the remaining salt. Bring everything back to a boil before reducing the heat to let it simmer until the potatoes are tender. Add in the roasted garlic cloves.
Remove about one cup of potatoes from the pot after they’ve cooked through. Smash them gently with a fork before returning them back into the soup or use an immersion blender for an ultra-smooth finish.
Ladle the soup into bowls and top with croutons, cheese, or fresh parsley if desired.