In a medium pot over medium heat, add potatoes and cover with about 2 inches of water. Boil potatoes until just fork tender with a little resistance, about 5 minutes then drain.

In another medium pot over medium heat, heat oil. Add onion, celery, and carrot and season with salt and pepper. Cook until soft, about 10 minutes. Add garlic, oregano, and red pepper flakes and cook until fragrant, 1 minute more.

Sprinkle flour over veggies and stir to coat. Slowly pour in milk and cream and stir until no flour lumps remain. Add broth and about half of the par-cooked potatoes. Season with salt and peper.

Bring to a boil then reduce heat and let simmer until potatoes are very soft and fall apart when pierced with a fork, about 10 minutes. Turn off heat and use an immersion blender to blend soup until completely smooth.

Return pot over medium heat and add remaining potatoes. Bring to a boil, then reduce heat and simmer, stirring often, until potatoes are soft, 5 minutes.