1. Heat the olive oil in a large (10-12 inch) oven-safe skillet over medium-high heat. Add the cubed chicken and cook for 5-7 minutes, stirring occasionally, until it’s browned on all sides and mostly cooked through. Remove the chicken from the skillet and set aside.

2. Add the chopped onion and carrots to the same skillet, reducing the heat to medium. Saute for 5-7 minutes, stirring occasionally, until the vegetables begin to soften. The onions should become translucent.

3. Stir in the dried thyme, black pepper, and salt with the softened vegetables. Cook for another minute until fragrant.

4. Sprinkle the all-purpose flour over the vegetables and stir constantly for 1-2 minutes. The flour will absorb the pan drippings and form a thick paste (a roux). Slowly pour in the chicken broth, whisking continuously to prevent lumps. The mixture will start to thicken as it heats.

5. Stir in the milk until well combined. Bring the mixture to a gentle simmer, then reduce the heat to low. Return the cooked chicken to the skillet, along with the frozen peas and corn. Stir everything together. Let it simmer for 5 minutes, stirring occasionally, until the sauce has thickened to your desired consistency and the vegetables are heated through. Taste and adjust seasonings if needed.

6. Carefully remove the skillet from the heat. Open the can of refrigerated biscuits and arrange them on top of the chicken and vegetable filling. You can place them in a single layer, slightly overlapping if necessary, to cover most of the surface.

7. Transfer the skillet to a preheated oven at 375 F (190 C). Bake for 12-15 minutes, or until the biscuits are golden brown on top and cooked through. The filling should be bubbly around the edges.

8. Carefully remove the hot skillet from the oven. Let it cool for a few minutes before serving directly from the skillet.