Preheat your oven to 375°F (190°C). Heat the olive oil in a large oven-safe skillet over medium-high heat. Add the chicken pieces in a single layer and cook for 4-5 minutes until golden brown and cooked through. Remove the chicken to a plate and set aside.

Reduce heat to medium. In the same skillet, add the diced onion, carrots, and celery. Sauté for 5-7 minutes until the vegetables start to soften and the onion becomes translucent. Add the minced garlic and cook for another minute until fragrant.

Add the butter to the skillet and let it melt completely. Sprinkle the flour over the melted butter and stir constantly for 1-2 minutes to create a roux.

Gradually whisk in the chicken broth and milk, stirring constantly to prevent lumps. Bring to a simmer and cook for about 5 minutes until the sauce thickens enough to coat the back of a spoon.

Stir in the dried thyme, rosemary, salt, and pepper. Add the cooked chicken and frozen peas to the skillet and stir until well combined. Adjust the seasoning if needed.

Transfer the skillet to the preheated oven and bake for 20-25 minutes until the filling is bubbly and the top is lightly golden. Let it rest for 5 minutes before serving.