Cut the carrots in half. Heat 2 tablespoons of oil in a large skillet over medium-high heat. Add the carrots and cook for 1 minute. Add the broccoli and cook for 2 more minutes. Season with salt and pepper and move the vegetables from the skillet to a mixing bowl. Set aside.
Return the skillet to the stove, and add the garlic. Stir until fragrant, about one minute. Add the wine and scrape the brown bits from the bottom of the pan, then add the chicken stock. Simmer for 3-4 minutes, until slightly reduced. Stir in the cream and Parmesan cheese until melted. Taste for seasoning and adjust with additional salt and pepper if needed.
Add the cooked vegetables to the sauce and stir to combine. If necessary, add more chicken stock. Place the cooked pasta in a large serving bowl and pour the contents of the skillet on top. Toss gently to combine. Serve immediately, with extra cheese on the side.
