Pound out the fatter area of the chicken breasts so they are even thickness and cook evenly on the griddle. Add the chicken breasts to a large zip top bag with ½ cup of the dressing and juice of half the lemon. Mix well to evenly coat the chicken, zip the bag, and marinate in the refrigerator for about 3-4 hours.
When chicken is done marinating, preheat griddle or large skillet over medium heat. For griddle cooking, the temperature should be about 375-400℉. Season the chicken breasts with your favorite all-purpose seasoning.
Cook the chicken breasts on the griddle, flipping about half way through cooking time, until the internal temp of each breast is 165℉. Then transfer to a cutting board to rest while you cook the vegetables and pasta.
Add about 2 tablespoons of oil to the griddle and spread it around with your spatula. Sauté the zucchini and shallots on the oiled surface. When those vegetables are about half way cooked through, add the artichoke hearts, sun-dried tomatoes, and grape tomatoes. When almost done cooking, move the vegetables to a cooler zone on the side of the griddle.
Add about 1 tablespoon of oil to the griddle. Add the refrigerated tortellini to the oiled griddle. Sauté for about 3-4 minutes. Then, add a squirt of water to the tortellini and immediately cover with a dome to steam.
When tortellini is about 3/4 of the way done, add the sautéed vegetables and pasta together on the griddle. Add ½ cup of the Italian dressing, ½ cup of heavy cream, and the basil to the pasta. Toss to combine and sauté for an additional 2-3 minutes for all of the flavors to come together and the sauce to thicken slightly. Then transfer to a serving platter.
Cut the cooked chicken breasts in slices against the grain. Add the cut chicken to the top of the pasta. Squeeze the juice of half a lemon on top. Tear burrata into bite-sized pieces and place on top of the chicken and pasta. Enjoy! *You can also drizzle on a bit more dressing if desired.