Preheat oven to 425°F.
Trim carrots and slice on bias or dice in bite-size pieces. Dress with a little olive oil and season with salt and pepper.
Clean carrot tops, trim stems and any brown edges. Reserve 1/2 cup.
Arrange snap peas on a large baking sheet and coat lightly with olive oil. Season liberally with salt and lots of fine black pepper.
Roast carrots and peas 15-20 minutes until tender and crispy at edges, but not browned all over.
Combine carrot tops, herbs, half the roasted peas, the stock and nuts in a food processor. Pulse the machine to finely chop. Add 1/4 cup olive oil and pulse to combine. Transfer to a large, warm, serving bowl and stir in cheese. Season with salt and pepper to taste.
Cook pasta in salted boiling water to just-shy of al dente. Add half a mug, about a cup, of starchy water to the serving bowl and stir to combine it with the pesto. Drain pasta and add to bowl along with the carrots and peas. Toss to coat, taste to adjust seasoning and serve.