Melt the butter in a soup kettle over medium-high heat. Add the bacon and cook until crisp. Scoop out the bacon and drain on paper towels, saving it for later.
Pour off all but 1/4 cup of the fat. Add the onions and green pepper with a pinch of salt and pepper and cook until soft. Add the garlic and cook 1 minute more. Sprinkle on the flour and mix into the vegetables.
Add the broth and potatoes. Cover, bring to a boil, then lower the heat and simmer 10 to 12 minutes until the potatoes are tender.
Add the shredded carrots and corn. Cover and simmer 5 to 6 minutes to blend the flavors.
Stir in the half-and-half. Season with the thyme, cayenne, more salt, and lots of black pepper. Sprinkle with parsley and the reserved bacon, give it one last stir, and ladle it up piping hot.