Cook the chopped bacon in a large pot or Dutch oven over medium heat until crisp. Remove the bacon with a slotted spoon and set it aside on a paper towel-lined plate. Leave 2 tablespoons of bacon grease in the pot.
Add the onion and celery to the pot with the bacon grease. Cook until softened, about 5 to 7 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the vegetables and stir constantly for 1 minute to cook out the raw flour taste.
Gradually whisk in the chicken broth until smooth. Bring the mixture to a simmer.
Add the diced potatoes and corn. Return the mixture to a simmer, then reduce the heat to medium-low, cover, and cook for 15 minutes, or until the potatoes are tender.
Stir in the heavy cream, salt, and pepper. Heat through gently for 3 to 5 minutes, but do not let it boil after adding the cream.
Taste and adjust seasoning if needed. Ladle the chowder into bowls and top each serving with the reserved crisp bacon and fresh parsley.
Notes
For a thicker chowder, mash about one cup of the cooked potatoes against the side of the pot before adding the cream.
If you prefer a less rich soup, substitute half-and-half for the heavy cream.
You can use frozen corn if fresh corn is not available.