On a work surface, arrange the salami slices in a single layer. Spoon heaping teaspoons of the goat cheese down the center of each slice.
In a medium bowl, toss the arugula with the olive oil and vinegar and season with salt and pepper. Divide the arugula among the salami slices and roll them up. Cut each roll in half crosswise, arrange seam side down on a platter and serve.