Finely chop the onion, peel and cut the potatoes into 1-inch pieces, and mince the garlic cloves. To prevent the potatoes from browning, place them in a bowl of cool water.
In a Dutch oven or a large pot, melt the butter over medium heat. Cook the onion until it becomes translucent, roughly 4 minutes. Add the minced garlic and cook for another 30 seconds.
Sprinkle the flour over the onions and garlic. Stir and cook the flour for 1-2 minutes.
Add the Italian seasoning, salt, pepper, chopped potatoes, carrots, celery and chicken broth to the pot. Stir thoroughly to dissolve the flour and scrape up any browned bits from the bottom of the pot.
Cover the pot with a lid and bring it to a boil. Once boiling, reduce the heat to medium and cook the vegetables for 10-15 minutes, stirring occasionally, until they are fork-tender.
Remove the lid and add the cooked chicken, frozen peas, and heavy cream to the pot. Stir well, cover again, and let it simmer for an additional 5 minutes.
Taste and adjust the seasoning if necessary. Optionally, garnish with fresh parsley and enjoy!