In a large pot, melt the butter over medium heat.
Add the chopped onion and carrots, sauté until soft.
Stir in the diced ham and cook for 5 minutes.
Add the diced potatoes and chicken broth to the pot.
Bring to a boil, then reduce heat and simmer for 15 minutes.
Once potatoes are tender, stir in the heavy cream.
Season with salt and pepper to taste.
Simmer for an additional 5 minutes to thicken.
Garnish with fresh parsley before serving.
Enjoy your warm bowl of ham and potato soup!