Preheat an oven to 400°F.
Wash and trim the ends off of eight large carrots and slice in half lengthwise.
Place on a baking sheet and drizzle with a little olive oil and a pinch of kosher salt. Toss the carrots to coat.
Roast the carrots for 20-25 minutes, flipping halfway through the cooking process.
While the carrots roast, make the pesto. Add the arugula, walnuts and garlic to a food processor and pulse until finely chopped. Scrape down the sides of the bowl and pulse again.
Next, add the olive oil, water, salt and red wine vinegar to the food processor and pulse until the pesto is smooth.
To serve, scatter the carrots onto a large platter and top with spoonfuls of pesto. Garnish the carrots with a pinch of chopped walnuts if desired. Enjoy!