In a large pot over medium heat, add olive oil or butter. Once melted, add chopped onion and cook for about 5 minutes until translucent. Stir in minced garlic and sauté for 1-2 minutes until fragrant.

Sprinkle flour over the sautéed onion and garlic mixture, stirring for 1-2 minutes to form a roux.

Gradually pour in broth while stirring to prevent lumps. Then add diced Yukon Gold potatoes, thyme, dill, salt, and pepper. Bring to a boil.

Lower the heat and simmer uncovered for 20-25 minutes until potatoes are fork-tender.

Optional: Use an immersion blender to partially puree the soup for a creamier consistency.

Stir in milk and cheese, allowing them to melt completely over low heat.

Taste and adjust seasoning as needed, then ladle the soup into bowls.