Fill a large pasta pot with water and place it over high heat. Once the water comes up to a boil, salt it and drop in the pasta. Cook the pasta to al dente according to package directions. Before draining the pasta, reserve a mug full of starchy cooking water, then drain and reserve.
While the water is coming up to a boil, place a large skillet over high heat with 3 turns of the pan of EVOO, about 3 tablespoons. Season the chicken pieces with the poultry seasoning, salt and pepper then add it to the preheated skillet. Cook the chicken until golden brown and cooked through, 3-4 minutes per side.
Once the chicken is brown, add the garlic and onions to the pan, and cook until softened, about 5 minutes. Add the tomatoes and cover the pan with a lid. Cook, stirring occasionally, until the tomatoes burst open and begin to release their juices, about 5 minutes (if they haven’t started to burst open by that time, mash them lightly with a potato masher or wooden spoon). Season the mixture with salt and pepper.
Add the drained pasta and reserved starchy cooking water (about 1 cup) to the skillet with the chicken and tomatoes, and toss over the heat until combined, about 1 minute. Remove the pan from the heat and stir in the basil, arugula, and cheese. Serve.