Place all ingredients, except the salt and pepper in the bowl of a food processor. Blend until the mixture is chunky, scraping down the inside of the bowl, if necessary. Season with salt and pepper, to taste.
Transfer the olivada to a small dipping bowl and place on a serving platter. Arrange the carrots, cucumber, fennel, and cherry tomatoes around the olivada. Serve.
Recipe courtesy of Giada De Laurentiis, 2008