Preheat oven to 350°F (180°C).
In a Dutch oven or oven-safe skillet, heat olive oil over medium heat. Add onion and cook for about 5 minutes, until soft and translucent.
1 tablespoon olive oil, ½ onion
Stir in garlic, carrots, and celery, and cook for another 7 minutes, until vegetables begin to soften. Add tomato paste and cook until slightly browned.
1 garlic clove, 2 carrots, 2 celery stalks, 2 tablespoons tomato paste
Stir in the cream of chicken soup, milk, thyme, salt, and pepper until well combined. Add the shredded chicken and peas, stirring to mix evenly.
1 10.5 oz can cream of chicken soup, ⅓ cup whole milk, 1 teaspoon thyme, Salt and pepper to taste, 1½ pounds cooked chicken breast, 1 cup peas
Arrange the biscuits on top of the mixture and brush them with melted butter.
8 uncooked canned biscuits, 2 tablespoons melted butter
Transfer the skillet to the oven and bake for 25 minutes, or until the biscuits are golden brown and fully cooked.
Sprinkle with fresh parsley before serving.
Fresh parsley