Make the cream sauce: in a saucepan over medium heat, melt butter and add garlic and cook for 1 minute. Add the heavy cream and parmesan, and whisk until you get a homogeneous sauce (1-2 minutes). Remove from heat and set aside.
Cook the chicken: In a large relatively deep skillet or dutch oven, heat olive oil over medium high heat, add the chicken and immediately season with italian seasoning, salt, and pepper.
Cook and stir the chicken until it’s fully cooked, about 4 minutes. Remove onto a plate and set aside.
Meanwhile, cook the pasta in salt water according to package directions. Reserve pasta water to thin out the sauce later if you need to.
To the same skillet or dutch oven, heat 1 tablespoon of olive oil, and add all the vegetables (except for cherry tomatoes if using), and cook for about 5 minutes. Add cherry tomatoes in the last 30 seconds.
To the vegetables, add pasta, and cream sauce (and pasta water if needed). Gently toss to combine, and add chicken, and toss again. Remove from heat, serve immediately.