Pour the olive oil on top and add salt and pepper to taste. Pour in the cream and broth, then stir everything together and top with the pats of butter. Place on the middle rack under the broiler until the vegetables are roasted and slightly browned.
At the same time, add the pine nuts to a small dry skillet over medium heat and toast them, stirring constantly, until golden brown, about 2-3 minutes. Remove them from the heat.
Remove the chicken and veggies from the oven and immediately pour the drained pasta into the dish. Spoon the pesto over the pasta and sprinkle the Parmesan on top.