Position a rack in the center of the oven and heat the oven to 375°F. Arrange the beets in a baking dish that’s just large enough to accommodate them, such as an 8-inch square glass baking dish. Drizzle the beets with the vegetable oil and turn to coat well. Cover the dish with foil. Roast the beets until tender when pierced with a paring knife, about 1 hour. Let cool.
Peel the beets and slice 1/4 inch thick. Combine the beets, olive oil, garlic, 1 Tbs. of the chives, and 1/2 Tbs. of the tarragon in a medium bowl. Season to taste with salt and pepper.
In a medium bowl, combine the goat cheese, crème fraîche, peppercorns, and the remaining 3 Tbs. chives and 1 Tbs. tarragon. Season to taste with salt and pepper and refrigerate until ready to use.
Position a rack 6 inches from the broiler element and heat the broiler on high. Split the ciabatta pieces and lightly toast them cut sides up directly on the rack under the broiler.
Divide the beet mixture evenly over the bottom halves of the bread. Drop the cheese mixture by spoonfuls over the beets. Top the cheese with the arugula, dividing evenly. Place the top halves of the ciabatta over the arugula and press gently. Cut the sandwiches in half on the diagonal and serve.
Make ahead: The goat cheese can be prepared up to 1 week ahead. The beets can be roasted up to 3 days ahead, and mixed with the oil and seasoning up to 1 day ahead. Keep everything refrigerated until ready to use.