With a julienne peeler, peel the carrots into thin, spaghetti-like strands. Cover with a damp tea towel or damp paper towel to avoid it drying out.
Add oil to a large skillet or wok, and preheat over medium. Add sliced leek and garlic and sauté for 3-4 minutes, until soft and translucent. Add a couple pinches of salt and several grounds of pepper.
Add the asparagus to the skillet and sauté for around 8 minutes more, until tender. Increase heat if necessary.
Then stir in the peas and cook until heated throughout.
Meanwhile, make the pesto. Add the garlic into a food processor and process until minced. Now add in the basil and sun-dried tomatoes and process again until smooth. Finally, add the rest of the ingredients and process again until combined and smooth.
Stir all the pesto into the vegetable skillet mixture and cook until heated throughout. Season to taste.
Serve the vegetable pesto mixture on top of the carrot pasta.