In a large soup pot or dutch oven over medium-high heat, cook the chopped bacon until done — about 5-8 minutes depending on the thickness of the bacon. Remove the bacon to a paper towel-lined plate, leaving about 2 tablespoons of bacon fat in the pot. Set bacon aside.
Lower heat to medium, adding the onion, carrot, and celery. Cook until vegetables start to soften, about 5 minutes.
Add garlic and thyme leaves, stirring until they become fragrant; just a minute or two.
Add flour, and stir. Cook for a couple of minutes to make a roux.
Add cooked chicken, corn, potatoes, and chicken stock. Stir until soup comes to a boil, and then lower the heat to a gentle bubbling simmer. Cook until potatoes are done, about 15 minutes.
Stir in heavy cream and add salt & pepper. Taste and add more if necessary.
Stir in half of the crumbled bacon, if using.
To serve, divide soup among 6 bowls. Garnish with more crumbled bacon and fresh chopped parsley.
Optionally, also garnish with shredded cheddar cheese.