Put the beets in an 8-inch square baking dish. Add the vinegar, salt, thyme sprigs and 3 tablespoons water to the baking dish. Toss well to coat. Cover the dish with aluminum foil and roast until the beets are tender all the way through, about 50 minutes. Allow the beets to cool slightly, then use a paper towel to rub off the skins. Cut the beets into quarters or sixths depending on the size. Toss with any of the remaining liquid from roasting. Set aside to cool slightly.
For the dressing: Heat a small skillet over low heat. Add the oil, shallots and 1/4 teaspoon of the salt and cook until the shallots are soft but not brown, about 5 minutes. Remove from the heat and cool for 5 minutes. Meanwhile, in a large bowl, whisk together the vinegar, Dijon mustard and remaining 1/4 teaspoon salt. Add the cooled oil mixture and whisk to combine.
For the salad: Add the arugula and beets to the dressing and toss gently to coat. Place the salad on a large platter and tear the burrata around the sides. Sprinkle with the pine nuts.