Peel carrots, reserving greens. Cut in half lengthwise, toss with oil and seasonings and place on a parchment lined baking sheet or in a clay baking dish. Bake at 400°F for 30-40 minutes, or until tender and lightly golden on the bottom.
Toast walnuts in a dry skillet over medium-high heat, tossing often until fragrant and just starting to brown, about 5 minutes. Set aside to cool.
For pesto, in a food processor combine the toasted walnuts and remaining ingredients except for the oil and salt. Pulse until coarsely chopped.
With machine running, add 1/3 cup of the oil and until pesto is finely chopped and well blended. To thin it out, add in more oil or some water until you get your desired consistency.
Season to taste with salt and add more lemon juice if needed. Drizzle (or toss) over hot roasted carrots.