In a large kettle or Dutch oven bring 4 quarts water to boil; add the 1 teaspoon garlic oil and salt. Add the spaghetti; then cook according to package directions.
Meanwhile, in a small saucepan, cook the carrots, covered in a small amount of boiling water, for 5 minutes. Add broccoli florets and cook for 3 minutes more; drain.
In another saucepan heat the 1/3 cup garlic oil over low heat. Add the cooked vegetables to the oil, stirring to coat well and heat through.
To serve, drain the spaghetti; return spaghetti to kettle; pour the vegetable mixture over pasta and toss. Transfer to individual plates. Sprinkle cheese and pepper over each serving.
