In a large pot, heat a couple of tablespoons of olive oil over medium heat. Add diced yellow onion and sauté for about 4-5 minutes, stirring gently until they become translucent and aromatic. Then, add minced garlic and cook for another minute.

Next, stir in dried thyme, dried parsley, and dried rosemary, along with a pinch of black pepper and salt. Sauté the herb mixture briefly for about 1-2 minutes.

Add diced Yukon Gold potatoes into the pot, pouring in vegetable broth until the potatoes are just covered. Bring the mixture to a boil, then reduce to a gentle simmer. Cook uncovered for 15-20 minutes, or until the potatoes are fork-tender.

Once the potatoes are tender, use an immersion blender to purée about half of the soup directly in the pot or carefully transfer half to a regular blender. Blend until smooth while leaving some potato chunks.

Reduce the heat to low before adding whole milk and shredded sharp cheddar cheese. Stir until the cheese has melted completely and the soup is smooth.

Ladle the warm soup into bowls and garnish with fresh parsley or thyme. Enjoy hot, alongside crusty bread or garlic toast.