Hillbilly: This slicer dates back to 1880, when it first wowed kitchen gardeners with its 1- to 2-pound, heavily ribbed fruits. The flesh is orange-yellow and mottled with red, with an almost peachlike texture.
In a small bowl, mix 2 tablespoons extra-virgin olive oil, 2 tablespoons balsamic vinegar, and 1 tablespoon minced shallots. Rinse and core about 1 1/2 pounds firm-ripe Hillbilly or similar tomatoes. Cut crosswise into 1/2-inch-thick slices. Arrange tomatoes, overlapping slightly, on a rimmed platter or plates. Drizzle dressing over tomatoes; add salt and pepper to taste. Garnish with baby arugula leaves, if desired.