Prep the vegetables: peel and dice potatoes; chop onion, celery, and carrot; mince garlic; dice the ham.
Warm butter and olive oil in a large heavy pot over medium heat until the butter melts.
Sauté onion, celery, and carrot with a pinch of salt until softened, about 6–8 minutes.
Stir in garlic and cook until fragrant, about 30 seconds.
Sprinkle in flour and cook, stirring, 1–2 minutes to form a blond roux.
Whisk in chicken broth gradually. Add potatoes, thyme, pepper, and the remaining salt. Bring to a boil, then lower to a simmer.
Simmer until potatoes are tender, 12–15 minutes. Lightly mash some potatoes in the pot to thicken.
Stir in ham, milk, and cream. Warm gently 5–7 minutes without boiling. Taste and adjust seasoning.
Rest 5 minutes. Ladle into bowls and top with parsley and cheddar, if desired.
Notes
Variation: Swap half the potatoes for cauliflower florets for a lighter bowl, or add a pinch of smoked paprika for extra depth. Storage: Refrigerate up to 4 days; reheat gently and thin with a splash of broth or milk if needed.This recipe is an original creation inspired by classic Ham and Potato Soup Delights flavors. All ingredient ratios and instructions are independently developed.