Heat olive oil in a large pot over medium heat, add diced yellow onion and sauté for about 4-5 minutes until translucent.

Stir in minced garlic and cook for an additional minute until golden and aromatic.

Add dried thyme, parsley, rosemary, black pepper, and salt. Stir for about 30 seconds.

Incorporate diced Yukon Gold potatoes and pour in vegetable broth. Bring to a boil, then reduce and simmer uncovered for 15-20 minutes.

Blend about half the soup with an immersion blender or in a separate blender until smooth, then return to the pot.

Stir in whole milk and shredded cheddar cheese over low heat until cheese has melted. Add butter if desired.

Ladle soup into bowls and garnish with fresh parsley or thyme.