Peel and cut potatoes into 1-inch chunks, dice onion into 1/2-inch pieces, and mince fresh garlic cloves.
Heat olive oil in a large pot over medium heat until shimmering.
Add diced onion and cook for about 8 minutes until soft and translucent, stirring occasionally.
Add minced garlic and 1/2 teaspoon salt, stir constantly for about 1 minute until fragrant, avoiding browning.
Pour in vegetable broth and bring to a boil over high heat.
Add prepared potatoes, the remaining 1/2 teaspoon salt, and fresh chopped parsley.
Reduce heat to medium-low and simmer uncovered for 15-20 minutes until potatoes are tender.
Add roasted garlic cloves, stirring gently to distribute them throughout the soup.
For chunky texture, remove 1 cup of potatoes, mash roughly, and return to pot. For smooth texture, blend entire soup carefully using an immersion blender.
Season soup with freshly ground black pepper and adjust salt to taste.
Ladle soup into bowls and garnish with optional croutons, grated cheese, and chopped parsley.