Heat oil in a large Dutch oven or soup pot over medium heat until it begins to shimmer. Add the onion and cook for 2 to 3 minutes, or until translucent and tender.
Add the garlic, thyme, parsley, and potatoes and cook an additional 30 seconds, stirring once or twice.
Quickly whisk in flour and cook another 30 seconds, stirring continuously. Pour in the half-and-half, chicken broth, cream, and bay leaf and bring to a boil.
Reduce heat to simmer. Stir in chicken and veggies and continue to simmer for 30 minutes, or up to 2 hours (check often to ensure liquid does not cook off).
Remove and discard bay leaf. Season to taste with salt and pepper (I like 1 teaspoon salt and 1/2 teaspoon pepper). Serve warm with buttermilk biscuits.