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Heat olive oil in a large skillet over medium-high heat. Add the diced onion, and sauté 4-5 minutes, until fragrant and translucent.
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Add the celery, carrots and sliced mushrooms to the skillet. Season the vegetables with a small pinch of salt. Sauté another 4-5 minutes, until the mushrooms start to soften. Remove the transfer the vegetables to a plate and set aside.
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Whisk together the half and half and cornstarch to form a slurry. Set it aside.
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Pour the chicken stock into the skillet and scrape any browned bits from the bottom of the pan. Bring the chicken stock to a simmer over medium-low heat.
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When the stock is simmering, slowly pour the slurry into the skillet, stirring constantly, until the sauce forms a creamy gravy that is thick enough to coat the back of a spoon.
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Season the gravy with Italian seasoning, salt, and pepper.
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Add the cooked veggies, cubed turkey and frozen peas to the skillet, and stir to combine. Stir over medium-low heat for about 4-5 more minutes, until the peas and turkey are warmed through
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Serve over biscuits, rice, or mashed potatoes