Cut chicken breast into bite sized pieces, season with 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper. Add 2 teaspoons of oil to a large skillet or cast iron pan and cook the chicken breast over medium heat for about 3 minutes on each side until browned and cooked through, 6-8 minutes total. Remove browned chicken pieces from the pan and set aside.
In the same pan, melt butter over medium heat, then add in shallots and carrots. Cook over medium-low heat until softened, stirring often, about 5 minutes. Add the peas and corn, and then mix in the all purpose flour until all the veggies are coated.
Pour in the broth and bring the mixture to a boil over high heat, then immediately lower it to a simmer over medium low heat, stirring often so the flour gets smooth and not clumpy. With the heat turned down to medium low, stir in milk as it starts to thicken, then add thyme and 1/4 teaspoon kosher salt and a pinch of black pepper if desired. Simmer for 8-10 minutes, stirring often, until the sauce is nice and thick, enough to coat a spoon. Add cooked chicken into the mixture. Taste the sauce and adjust the seasonings to your preference.
If using an oven-safe skillet, top the crustless pot pie mixture with panko and broil in the oven on high heat for 1-2 minutes, until the panko is golden brown. If using individual ramekins or a casserole dish, transfer the filling to the dish and top with the panko, broiling the same way. Serve warm.
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Notes
Cooked chicken short cut - Use cooked rotisserie chicken or any leftover chicken and stir it in step 3 after the sauce has thickened.
Frozen veggies short cut - Fresh is definitely more flavorful and a better texture, but for a very quick meal with no chopping, you can use 2 cups of a frozen vegetable medley. You can also substitute the fresh chopped vegetables with a mirepoix that is store-bought.
Dairy free - Substitute oat milk and olive oil or other favorite sub for butter. Use oat milk as a replacement for whole milk.
Gluten free - Use gluten free panko (brand recs in post) and arrowroot or cornstarch to thicken the sauce instead of flour.