Preheat the oven to 375°F (190°C) and set a rack in the center of the oven.
In a medium saucepan over medium heat, melt the butter until fully melted.
Add the diced onion and carrot and cook for 4–5 minutes, stirring occasionally, until softened.
Add the minced garlic and cook for 1 minute, stirring constantly, until fragrant.
Sprinkle the flour evenly over the vegetables and stir continuously for 1 minute to coat everything evenly.
Slowly pour in the chicken stock while whisking to prevent lumps, then cook for 2–3 minutes until the mixture thickens.
Stir in the heavy cream, salt, black pepper, and thyme, and allow the mixture to gently simmer for 1–2 minutes until creamy.
Add the shredded chicken and frozen peas and stir until fully combined.
Remove the filling from the heat and transfer it into a 10-inch cast iron skillet, spreading it into an even layer.