Preheat oven to 375°F (190°C).
Heat olive oil in a large oven-safe skillet over medium heat.
Add diced onion and cook for 3–4 minutes until soft.
Stir in garlic and cook for 30 seconds until fragrant.
Add carrots and cook for another 3 minutes.
Melt butter in the skillet and sprinkle flour over the vegetables.
Stir well to create a light roux and cook for 1 minute.
Slowly pour in chicken broth while stirring continuously.
Add milk and mix until the sauce thickens.
Stir in shredded chicken, peas, salt, pepper, and thyme.
Place biscuit dough pieces evenly on top of the chicken mixture.
Transfer the skillet to the oven and bake for 18–20 minutes until biscuits turn golden brown.
Remove from oven and sprinkle with chopped parsley before serving.