Bring a large pot of water to a boil. Add pasta and cook for 5 minutes. Add cauliflower florets and cook until the pasta and florets are tender, about 4 minutes more. Drain, rinse, and return to the pot.
Meanwhile, heat oil in a large saucepan over medium heat. Add onion and cook, stirring, until tender, 2 to 3 minutes. Add wine and cook until reduced slightly, about 1 minute. Whisk milk, flour, salt, and pepper together in a medium bowl and add to the pan. Bring to a boil over medium-high heat, stirring frequently. Cook, stirring, until thickened, about 1 minute. Reduce heat to low and stir in cheese until smooth. Stir chicken (or turkey) and mustard into the cheese sauce; cook until heated through, about 2 minutes.
Stir the sauce into the drained pasta and cauliflower. Serve sprinkled with chives (or scallion greens).
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Cheesy Chicken (Or Turkey) Pasta With Cauliflower (cont.)