In a large pot or Dutch oven, heat butter and olive oil over medium heat. Add onion, carrots, and celery. Cook for 5–6 minutes until softened. Add garlic and cook for another 30 seconds.
Sprinkle flour over the veggies and stir well to coat. Cook for 1–2 minutes to eliminate the raw flour taste.
Gradually whisk in the chicken broth. Stir until the mixture is smooth and begins to thicken. Add thyme, parsley, salt, and pepper. Simmer for 10–15 minutes, stirring occasionally.
Add shredded chicken, peas, and corn to the pot. Simmer for another 5 minutes until heated through.
Reduce heat to low and stir in the heavy cream. Let it warm through, but do not boil. Taste and adjust seasoning if needed.
Ladle the soup into bowls and serve with biscuits or puff pastry for dipping.