Preheat the oven to 400°F.
Bring a pot of salted water to a boil and cook the pasta according to package directions. Reserve about ¾ cup of pasta water before draining.
While the pasta cooks, add the broccoli and cherry tomatoes to a baking dish. Drizzle with the olive oil and sprinkle with salt and pepper. Toss to coat.
Place the Boursin cheese in the center of the dish.
Bake for 20 to 25 minutes, until the broccoli is tender and the tomatoes have burst.
Remove from the oven and mash the Boursin into the vegetables to create a creamy sauce.
Add the cooked pasta, cooked chicken, and about 1/4 cup of the reserved pasta water. Toss until everything is evenly coated. Add more pasta water if needed to loosen the sauce.
Stir in the parmesan cheese and serve warm.