Make the cream sauce: In a saucepan over medium heat, melt butter. Once melted, add garlic and cook for about one minute, just until it becomes fragrant. Next, pour in the heavy cream and add parmesan. Whisk the mixture together for one to two minutes until you achieve a homogeneous sauce. Remove from heat and set aside.
Cook the chicken: In a large skillet or Dutch oven, heat olive oil over medium-high heat. Add the diced chicken and season immediately with Italian seasoning, salt, and pepper. Stir and cook the chicken until it is fully cooked, which should take about four minutes. Once done, remove the chicken onto a plate and set aside.
Meanwhile, cook the pasta: In a pot of boiling salted water, add the dried pasta. Cook according to the package directions until al dente. Before draining, reserve a cup of the starchy pasta water to use later if needed.
Prep the vegetables: While the pasta is cooking, return to the skillet or Dutch oven. Add another tablespoon of olive oil if necessary and toss in the prepared fresh vegetables. Cook these for about five minutes, stirring occasionally. If you’re using them, add cherry tomatoes in the last thirty seconds of cooking to keep them fresh.
Combine everything: Once the vegetables are tender, add the drained pasta to the skillet along with the cream sauce. If you need to thin the sauce, pour in some of the reserved pasta water. Gently toss everything together until well combined. Finally, add the cooked chicken back into the pan and toss again to ensure everything is coated in the creamy goodness. Remove from heat and serve immediately.