Coat beets lightly with oil, put into baking dish with onion, bay leaves, garlic, parsley, thyme, peppercorns, 1 tsp salt, 1/2 cup water. Cover tightly and bake until the beets are tender, 45 minutes or more. Peel beets while warm. Strain juices in baking dish and reserve.
Cut a slice off both ends of each orange. Remove all the peel and white pith by slicing from top to bottom all the way around the orange. Quarter each peeled orange.
Put the beets, oranges and stained juices into a blender and blend well. With blender running, add the oil and 1 cup water through the opening on the lid and blend until smooth. Strain through a fine toothed sieve and season with salt.
Divide among 6 bowls. Top each with a pinch of flaky salt and a drizzle of olive oil. Garnish with cilantro and flowers.