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Combine half and half, chicken broth and seasoning in a large measuring cup with a spout and set aside.
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Slice the chicken in half lengthwise to create 2 to 3 thinner slices. Place plastic wrap over the chicken and pound each side to ¾ inch thickness. Pat each side dry.
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Season with salt, pepper and Italian seasoning. Sprinkle each side of chicken with flour.
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Heat olive oil in a large skillet over medium-high heat. Add the chicken and sear until a crust develops, 3 to 4 minutes per side. Set aside and let is rest for 10 minutes, then cut into strips.
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Cook the pasta and set aside.
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Add the wine to the skillet and then set the heat to medium. Bring to a gentle bubble and reduce by half, about 3 to 4 minutes.
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Add the butter and garlic to the skillet and cook for 1 minute. Add the flour and stir continuously for 2 minutes, until the raw flour smell is cooked off.
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Add the chicken broth mixture in a small amount at a time, stirring continuously. Do this slowly to keep the roux intact and maintain a thick consistency.
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Bring to a gentle bubble, then reduce heat to low and cover partially.
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Gradually sprinkle the cheese into the sauce, stirring continuously.
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Add the pasta and toss to incorporate. Then add the cooked chicken with any juices from the pan.