Preheat your oven to 375°F (190°C). Heat the olive oil in a large 12-inch oven-safe skillet over medium-high heat. Add the chicken pieces in a single layer and cook for 4-5 minutes, stirring occasionally, until they're golden brown and just 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 the mixture to a simmer and cook for about 5 minutes, stirring frequently, 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 everything together until well combined. Taste and adjust the seasoning if needed.

Transfer the skillet to the preheated oven and bake for 20-25 minutes, until the filling is bubbly around the edges, the top is lightly golden, and the internal temperature reaches 165°F. Let it rest for 5 minutes before serving.