Start by cooking the chicken. Butterfly the chicken breasts in half to make thinner cutlets. Season both sides with the Italian seasoning, salt, and pepper.
Heat 1 tbsp butter and 1 tbsp olive oil (for searing) in a skillet over medium-high heat. Sear the chicken for 3–4 minutes per side, until each side has a nice golden crust. The chicken does not need to be fully cooked through at this stage.
Remove the chicken from the pan and set aside. Once slightly cooled, chop it into bite-size pieces. It will finish cooking later in the sauce.
In a large pot or Dutch oven, melt 1 tbsp butter and 1 tbsp olive oil (for sautéing) over medium heat. Add the carrots, celery, onion, and 1 tsp salt. Sauté for 5–7 minutes, until the vegetables begin to soften.
Add the garlic and diced potatoes and cook for another 3 minutes.
Push the vegetables to the side of the pot. Add 3 tbsp butter to the empty space and let it melt. Sprinkle the flour over the butter and stir for about 1 minute to cook the flour and form a roux. Stir the vegetables into the roux so everything is lightly coated.
Pour in the chicken stock and heavy cream, stirring well. The mixture should begin to thicken.
Add the turmeric, sage, thyme, and the remaining 1 tsp salt. Stir well, then add the chopped chicken back to the pot.
Cover and simmer for 10–15 minutes, stirring occasionally, until the potatoes are tender and the chicken is fully cooked. If the filling becomes too thick, add a splash of milk, cream, or broth to loosen it.
Stir in the frozen peas and cook for 2–3 minutes, just until heated through.
Serve warm with fresh biscuits on the side.