Dice the carrots, celery, and onion. Cube the smoked ham and mince the garlic.

In a large pot over medium heat, melt the butter. Add the diced carrots, celery, and onion, and cook for about 5 minutes until the vegetables begin to soften. Add the cubed ham and garlic, stirring for another 1–2 minutes until fragrant.

Sprinkle the flour over the vegetables and ham, stirring continuously for about 3 minutes. The flour will thicken the base and remove any raw taste.

Pour in a splash of chicken broth, stirring constantly to prevent lumps, then add the remaining broth and water. Increase the heat to medium-high, bringing the mixture to a simmer. Let it cook for about 15 minutes to develop the flavors.

Dice the potatoes into half-inch cubes and add them to the pot. Let the soup simmer for 15–20 minutes, or until the potatoes are fork-tender.

Season the soup with salt, pepper, paprika, and dried thyme. For a heartier consistency, use a potato masher to mash some of the potatoes directly in the pot, creating a creamy base with chunky bits.

Stir in the heavy cream and reduce the heat to low. Let the soup warm through for about 5 minutes. Taste and adjust the seasoning if necessary.

Ladle the soup into bowls and garnish with freshly chopped parsley, a dash of paprika, and shredded cheese. Serve with crusty bread for the ultimate comfort meal.