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Add the olive oil to a large skillet (at least 13 inches) or a dutch oven over medium heat. Add the onions and cook until softened, about 3-4 minutes, then add the garlic and along with the carrots, celery, potatoes and the rosemary and thyme sprigs. Season with salt and pepper and then cook for 7-8 minutes until the vegetables have softened.
Sprinkle in the flour, stirring to coat the vegetables and cook for 1 minute. Slowly pour in the wine to deglaze the skillet (or pot) scraping up the bottom. Pour in the chicken broth, stir again and bring to a simmer.
Cut the chicken breasts into strips, 2 or 3 strips depending on how big the chicken breasts are, then carefully add them to the broth. Bring to a simmer, cover and cook for 20-25 minutes, stirring in between to make sure the vegetables aren’t sticking.
Remove the chicken from the broth and place onto a board or plate. Shred the chicken into large pieces and then stir the shredded chicken back into the stew. Simmer the stew for 5 minutes to let the flavors combine. Add the cream if desired and serve.