Preheat the oven to 450 degrees F.
Toss the carrots and cauliflower in a bowl with 3 teaspoons of the oil, the thyme, 1/2 teaspoon salt and 1/4 teaspoon pepper until well coated. Spread in a single layer on a rimmed baking sheet.
Roast the vegetables until tender and lightly browned, about 25 minutes, stirring once or twice. Season with more salt and pepper.
Meanwhile, cook the walnuts in a small skillet over medium heat, stirring, until toasted, about 5 minutes. Pour into a small bowl and toss with the parsley, lemon zest and remaining 1 teaspoon oil. Sprinkle over the roasted vegetables.