Preheat Pot: Heat oil in a large pot or Dutch oven over medium heat.
Cook Chicken: Add chicken to pot and sprinkle ½ teaspoon salt and ¼ teaspoon pepper on top. Cook until chicken is cooked throughout, about 5-6 minutes, turning chicken over to cook all sides as it cooks. Then, using a slotted spoon or tongs, transfer cooked chicken to a plate and set aside.
Sauté Vegetables: Add diced potatoes, carrots, celery, and onion into the same pot. Stir vegetables together and sauté until onions start to look translucent, about 3-4 minutes.
Add Seasonings: Stir in remaining 1 ½ teaspoons salt, remaining ¼ teaspoon pepper, thyme, parsley, garlic powder, and paprika, and cook for an additional 1 minute.
Add Flour: Sprinkle flour directly over sautéed vegetables and stir well to coat, cooking for 1 minute. (This is done instead of making a separate roux.)
Stir in Broth, Add Chicken, Then Simmer: Pour in chicken broth, stirring constantly to avoid lumps from forming. Add cooked chicken back in. Bring to a simmer, then let it cook until potatoes are tender, about 15 minutes, stirring occasionally.
Stir in Frozen Vegetables: Stir in frozen corn and peas and cook for 3-4 minutes.
Stir in Heavy Cream: Stir in the heavy cream and let it simmer for another 2-3 minutes. Carefully taste and add more salt and pepper, based on taste preferences.
Serve: Ladle soup into bowls, garnish with pepper and parsley, then serve.