In a 5 to 6 quart Dutch oven or soup pot, cook bacon until crisp over medium heat. Line a plate with paper towels while the bacon is cooking.
Remove bacon from pot using a slotted spoon and transfer to the plate lined with paper towels to drain. Leave bacon drippings in pot.
In the same pot with the drippings, melt the butter. Increase heat to medium high and add onions, carrots, and celery. Cook, stirring frequently, until onions are softened (about 4 to 5 minutes). Add garlic and cook until fragrant (about 30 seconds), stirring constantly.
Sprinkle the flour over the vegetables and stir to coat evenly. Pour in chicken broth and clam juice. Add dill, thyme, bay leaf, and potatoes. Stir to combine.
Bring to a simmer and cook for 12 to 15 minutes, or until potatoes and carrots are tender, stirring occasionally. Reduce heat as necessary to maintain a strong simmer.
Stir in the chopped clams (with their juices) and heavy cream. Cook just until heated through, while stirring occasionally. Season with salt and pepper. Remove and discard bay leaf.
Serve topped with bacon and chopped parsley.