Preheat oven to 400F. Make the dressing: whisk orange juice, lemon juice, 1/4 tsp. kosher salt, and 1/4 cup olive oil.
Place unpeeled red beets (rinsed, tops removed) in a baking dish. Cut 1/2 orange into 4 slices and arrange around beets. Top with a few fresh thyme sprigs, 1 tsp. kosher salt, and 3 Tbsp. olive oil. Pour 1 cup water over beets and cover with foil. Poke a few holes in the fiol and roast for 45-60 minutes.
Uncover beets and rub skin off with a paper towel once cool enough to handle. Cut into wedges.
Slice watermelon radish and place on plate with beets, buffalo mozzarella, and torn basil leaves. Garnsih with orange slices and finish with salt, pepper, and dressing.