Cook pasta in large saucepan as directed on package, adding broccoli during the last 3 minutes of cooking. Drain well.
Meanwhile, bring half-and-half to simmer in medium saucepan on medium heat. Reduce heat to medium-low. Add cream cheese, marjoram, garlic powder, rosemary, thyme, and sea salt; whisk until cheese is melted and sauce is well blended. Add chicken; simmer until heated through.
Place pasta and broccoli in large serving bowl. Spoon sauce evenly over pasta mixture. Toss gently to coat well. Sprinkle with Parmesan cheese and serve immediately.