In a large pot or Dutch oven, heat butter on medium high heat. Once hot, add chopped onions, sliced carrots and celery and sauté for 3-4 minutes, until tender.
Add the minced garlic and sauté for an additional minute, until fragrant. Mix in the flour until fully incorporated.
Pour in the chicken broth, water, bay leaves, salt, pepper, Italian seasoning, garlic powder, and paprika to the pot. Bring the liquid to boil.
Once boiling, add the chicken and cook for about 10-15 minutes, until the chicken is cooked through.
Carefully remove the cooked chicken from the pot and transfer it to a plate.
Add in cubed potatoes and cook for 12 minutes, until tender. Meanwhile, shred the chicken. (If you prefer, place the chicken in a bowl and use a hand mixer on high speed to shred it.)
Once the potatoes are tender, add the shredded chicken, corn, peas, freshly chopped greens and heavy whipping cream to the soup and bring to a light simmer. (Taste to see if you want to adjust the seasoning, as desired.)
Remove the soup from the heat. Serve hot or warm with desired sides.