Preheat the grill. Lightly butter a 20x30cm baking dish.
Bring a large pot of lightly salted water to a boil. Add pasta, cook for 8 minutes, then stir in broccoli and cook 3 minutes more. Drain and return to the pot.
Meanwhile, heat the olive oil over medium heat and stir in the garlic. Cook and stir until the garlic has turned golden-brown, about 3 minutes. Pour in white balsamic vinegar, chicken stock, salt and pepper. Bring to a boil then pour over the drained pasta and broccoli. Stir in the butter, pine nuts and half of the Parmesan cheese, then pour into the prepared baking dish. Sprinkle with remaining cheese.
Grill in preheated oven until the cheese has crisped and turned golden brown, about 4 minutes.