Preheat the oven to 375°F.
In a large, 12-inch oven-safe skillet, melt 3 tablespoons of butter over medium heat.
Add the diced onion, carrots, and celery. Cook for 7–9 minutes, stirring occasionally, until the vegetables begin to soften.
Add the minced garlic and cook for another minute.
Sprinkle the flour over the vegetables and stir until everything is evenly coated. Cook for 1 minute.
Slowly pour in the chicken broth, stirring continuously to prevent lumps.
Stir in the milk, heavy cream, thyme, poultry seasoning, salt, and black pepper.
Simmer for 3–5 minutes until the sauce begins to thicken.
Add the shredded rotisserie chicken and frozen peas, if using. Stir to combine and simmer for another 3–5 minutes. Remove from heat.
Open the can of flaky-layer biscuits. Gently separate each biscuit into 2 thinner layers and tear each layer into 2–3 smaller pieces.
Scatter the biscuit pieces evenly over the chicken pot pie filling, leaving small gaps between them.
Brush the biscuit topping with melted butter.
Bake uncovered for 20–25 minutes, or until the biscuit pieces are golden brown and fully cooked in the center. If the tops brown too quickly, loosely cover with foil.
Remove from the oven and let rest for 5 minutes.
Garnish with fresh parsley and serve warm.