In a large Dutch oven or heavy-bottomed pot, melt the butter with the olive oil over medium heat. Add the chopped onion, celery, and carrots (this is your mirepoix). Cook, stirring occasionally, for 8-10 minutes until softened and the onion is translucent.

Add the minced garlic and cook for another minute until fragrant. Be careful not to let it burn.

Add the cubed Yukon Gold potatoes, broth, bay leaf, 1 tsp kosher salt, and ½ tsp black pepper to the pot. Stir to combine.

Increase the heat to bring the soup to a gentle simmer. Once simmering, immediately reduce the heat to low. Cover the pot and let it cook for 15-20 minutes, or until the potatoes are completely tender and can be easily pierced with a fork. Avoid a rapid boil, as this can make the potatoes mealy.

Remove the pot from the heat and discard the bay leaf. Use an immersion blender to blend the soup directly in the pot until it reaches your desired consistency—either perfectly smooth or with a few small chunks left for texture.

If you don’t have an immersion blender, carefully transfer the soup in batches to a regular blender. Important: Remove the small cap from the blender lid and cover the opening with a folded kitchen towel to allow steam to escape. Blend until smooth, then return the pureed soup to the pot.

Place the pot back over low heat. Stir in the whole milk or half-and-half. Heat gently for a few minutes until warmed through, but do not let it boil. Taste and adjust seasoning with additional salt and pepper if needed.

Ladle the soup into bowls and serve hot, topped with your favorite garnishes like fresh chives, bacon, or shredded cheese.