Preheat oven to 400 degrees. Scrub beets and place in a pie plate or a baking dish with 1/2 inch of water. Tightly cover with foil and roast beets until tender, about 45-50 minutes. You should be able to insert a paring knife easily into the center of the largest beet.
Set beets aside uncovered until cool enough to handle. Peel and slice crosswise as thinly as possible.
Make the vinaigrette: whisk together all ingredients until emulsified or shake in a screw top jar.
Place the arugula on a platter and drizzle with just enough dressing to coat lightly.
Tuck the slices of persimmon and beets throughout the greens.
Tear the burrata into bitesize pieces and arrange over the salad.
Scatter the walnuts over the salad and drizzle with a little more dressing. You may not need to use all the dressing.
Sprinkle salad with a couple pinches of Maldon salt.