In a large pot, combine the diced potatoes, chopped onion, celery, carrots, minced garlic, and chicken broth. Place it over medium-high heat and bring the mixture to a rolling boil.
Once it reaches a boil, lower the heat to medium-low, allowing the soup to simmer for 15-20 minutes, or until the potatoes are tender enough to be easily pierced with a fork.
Using a potato masher, gently mash part of the potatoes in the pot to create a creamy texture, while leaving some chunks for added heartiness.
Stir in the heavy cream, sour cream, dried thyme, and smoked paprika. Season with salt and pepper to your preference, ensuring the flavors are balanced.
Let the soup simmer for an additional 5 minutes, allowing all the ingredients to meld together while stirring occasionally to prevent sticking.
Serve the creamy potato soup steaming hot, artfully garnished with a sprinkle of shredded cheddar cheese and a scattering of chopped green onions on top for a fresh finish.
Notes
For a vegetarian option, use vegetable broth instead of chicken broth.