How to Make It
Cook pasta according to package directions, omitting salt and fat. Drain pasta, reserving 1/4 cup cooking liquid.
Place shallot and garlic in a small bowl. Pour 1/4 cup reserved pasta cooking liquid over shallot mixture; steep 5 minutes.
Place pasta and cheese in a large bowl; toss to combine. Stir in chicken, vinegar, shallot mixture, 1/4 teaspoon pepper, and salt.
Combine oil and arugula. Add arugula mixture to pasta mixture; toss to combine. Sprinkle with remaining 1/8 teaspoon pepper and tomato.