Make the pesto: Add all the ingredients except the olive oil into a food processor bowl, pulse until thick paste forms. Add the olive oil and whisk by hand until combined or mix briefly in the food processor at low speed. You can also make the pesto using a pestle and mortar.
Cook the pasta until al dente (follow the package directions). The pasta should be cooked but still slightly firm in the center). Reserve a couple of tablespoons of pasta cooking water.
Cut the zucchini in half lengthwise and then slice crosswise into 1/4 inch / 5 mm slices.
Peel the carrots with a vegetable peeler and use the same peeler to make long, thin strips. Firmly hold the zucchini flat against a cutting board, press the peeler against it and peel the flesh, sliding the peeler away from you.
Heat the oil in a big frying pan over high heat, add the zucchini and cook for about 3 minutes, then add the carrots and cook for about 3 minutes. The vegetables should be browned and tender but still crunchy.
Add the cooked pasta and pesto to the vegetables along with a couple of tablespoons of pasta cooking water. Stir everything together, take the pan off the heat, season the pasta to taste with salt and pepper.
Serve sprinkled with grated Parmesan cheese and toasted pumpkin seeds.
Enjoy!