For the beet powder, completely crisp the beet slices overnight in a dehydrator. Combine the dehydrated beet with salt and pulverize in a coffee grinder. Sieve the powder and store in an airtight container.
For the pickled beet petals, whisk the pickling ingredients together in a non-reactive bowl until the salt and honey have dissolved. Add the beet slices and refrigerate for a minimum of 2 hours. Pickled beets may be held in their liquid for 1 week under refrigeration.
For the beet cloud, combine the sushi rice and dashi in a small pot and bring to a simmer. Allow the rice to cook over low heat until it has absorbed all of the liquid. Purée the now thick porridge in a blender, adding a small amount of liquid if necessary. With an offset spatula, spread a thin layer on a Silpat baking sheet (or silicone baking mat). Place the tray in the dehydrator at 140 degrees to dry. Dry until sheet pulls away easily from the Silpat. If there are any tacky areas in the center give it another hour. When dry enough to tear, portion the rice into 2-inch strips. Heat the grapeseed oil to 375 degrees and fry until the rice puffs crisp (they will quickly float to the surface). Drain the “clouds” on paper towels and dust with the beet powder.
Bring 2 quarts of seasoned water to a boil and prepare an ice bath for the kale and nori purée. Blanch the kale for 3-4 minutes until tender, then place kale in a colander and shock in an ice bath to set color and arrest cooking. Squeeze as much water as possible from the kale. Roughly chop the kale and nori and transfer them to a blender. Add salt, and with the motor running low, slowly add the oils to emulsify. Fold in the lemon zest and adjust seasoning with sea salt and lemon juice.
For the soba noodles, bring 6 cups of water to a boil—do not salt the water, the soba noodles are seasoned—add soba noodles and cook until al dente (approximately 5 minutes). Meanwhile, whisk together ponzu, tamari, benne seeds, citrus and oils until combined for vinaigrette. Set aside. Drain the soba noodles in a colander set in an ice bath and then rinse once more under cool water (all excess starch must be removed). Toss the noodles just prior to serving with the vinaigrette and chives; reserve.
Center a tablespoon of the purée into six chilled sake cups, then place 3 pickled beet petals over the purée. Nest the dressed soba noodles onto small forks or chopsticks and carefully transfer to the cup. Quenelle one heaping half teaspoon of caviar (approximately 5 g) into each cup and garnish with the beet cloud, additional benne seeds and scallion.