Melt butter in pot over medium heat. Add carrot, celery, and onion. Cook until the vegetables have begun to soften and onions are translucent. Add garlic and cook for a minute longer.

Sprinkle flour over the mixture and cook for three to four minutes, stirring often, until mixture appears dry and has lost it’s floury taste. Add broth in increments, stirring. Bring to a simmer and add potatoes and ham, salt and pepper to taste and the dash of hot sauce or pinch of cayenne.

Simmer gently for 15 – 20 minutes, until potatoes are soft and tender, stirring occasionally. Mash some of the potatoes with a masher or against the side of the pot until desired consistency. The slightly mashed potatoes will help thicken the soup. Optional, but simmering for about four or five minutes after mashing thickens the soup considerable. Turn off the heat and add cream or half & half, but do not boil after adding. Taste for seasoning and adjust for salt and pepper.

Garnish as desired, with the cheese or thinly sliced green onions or chives. If desired, simply place out for diners.

Note: this chowder will thicken up once refrigerated. If there are leftovers, you may need to thin with water, stock, milk, or additional cream or half & half, your choice.