Step 1To make the panna cotta, in a very small dish sprinkle the powdered gelatin over the surface of the cold water. Place the dish in the refrigerator to allow the gelatin to bloom.
Step 2Meanwhile, heat a small saucepan over medium-low heat. Add the butter to melt, then stir in the leeks and salt. Cook the leeks until they have wilted, but do not allow them to brown, about 5 minutes
Step 3Add the sliced sunchokes, then add enough water to just barely cover. Raise the heat and cook until almost all of the water has evaporated. Add the cream to the pan and bring to a gentle simmer and reduce by about a third.
Step 4Transfer the mixture to a blender and blend until it is very smooth. Strain the purée through a fine mesh strainer to obtain 1 cup of purée. If you have less than one cup, heat a little bit of cream to add to the purée to bring back to 1 cup of volume. Adjust the seasoning if necessary. While the mixture is still hot (if the mixture has cooled you can reheat it), use a spoon or small rubber spatula to slowly stir in the bloomed gelatin until it is dissolved and thoroughly incorporated. Take care not to stir air into the mixture and create bubbles.
Step 5Select four small serving bowls, and spoon 1½ to 2 ounces of the mixture into each bowl. Gently tap the bottoms of the bowls on a towel-lined flat surface to level out the panna cotta mixture and dislodge any air bubbles. Place the dishes on a flat shelf inside the refrigerator where they will not be disturbed as the gelatin sets, about a half hour. Once the gelatin is set, cover the bowls with plastic wrap to prevent a skin from forming on the surface. The panna cottas can be made up to 1 day before serving.
Step 6To make the topping, combine the grated sunchokes and the vegetable oil in a small sauce pot. Make sure that the level of the oil does not exceed one-third of the pot's depth. Slowly heat the pot to 300 degrees and frequently stir the sunchokes so that they do not clump together or accumulate on the bottom of the pan. Continue to cook until the bubbling subsides and the sunchokes are golden brown. Pour the sunchokes and oil through a strainer and collect the oil in a heatproof container. Drain the fried sunchokes on a plate lined with paper towels, then return the oil to the pot.
Step 7Heat the oil to 325 degrees and add the sunflower seeds. Fry the sunflower seeds until they are golden brown, then strain and drain them as you did for the sunchokes. Return the oil to 325 degrees and fry the panko crumbs until they are golden, then strain, drain and discard the oil. When the sunchokes, sunflower seeds and panko have cooled, gently combine them in a small mixing bowl and season them lightly with salt and pepper. Store the topping in a dry, airtight container until needed. The topping can be prepared a day in advance.
Step 8When you are ready to serve the panna cotta, place a heaping tablespoon of the bread crumb topping around the perimeter of the panna cotta (leaving a small area in the center bare) to make a "nest." Form a generous quenelle of caviar, and set it in the center. Serve immediately.