In a large saucepan, heat oil over medium heat. Add the bacon and cook until browned, about 3 minutes, scraping off any bits of bacon that stick to the bottom of the pan with a wooden spoon.
Next, add the onions, celery, and garlic. Cook and stir until vegetables become fragrant and begin to soften, about 3 minutes.
Add broth, potatoes, thyme and poultry seasoning. Bring to a boil, then reduce heat to low and simmer, covered, for 10 minutes.
Add the frozen corn kernels, peas and carrots. Simmer for an additional 5 minutes.
Stir in chopped chicken.
In a measuring cup or bowl, whisk together evaporated milk and cornstarch until smooth with no lumps. Add to chicken and vegetable mixture in the pot. Increase heat so that the soup comes to a gentle simmer and begins to thicken. Stir often.
Add parsley and season with salt and black pepper, to taste. Serve hot with desired toppings.