Place tortellini and chicken in a large bowl.
Combine garlic and salt on a cutting board. Mash with the side of a knife to form a paste. Place in a small bowl. Add oil, rind, juice, sugar, and pepper; stir with a whisk.
Add 2 tablespoons dressing to tortellini and chicken; toss to coat. Gently fold in arugula, shallot, and remaining dressing. Sprinkle with shaved Parmesan cheese.
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