Rinse and scrub the potatoes and then pat them dry. Place the salt in a large bowl and place a piece of parchment paper or aluminum foil on your work surface. Combine the fennel, coriander, star anise, and cardamom seeds in a large skillet or pan and set it over medium heat. Let it warm, occasionally tilting the pan to toss or swirl or scuttle the spices around so they toast evenly, until the spices are fragrant, 2 to 3 minutes. Tip the spices onto the parchment paper or foil and let cool. Grab the edges of the paper or foil and tilt half the cooled spices into a spice grinder. Coarsely grind them and pour them into the bowl of salt. Repeat with the remaining spices.
Finely grate the zest from the orange, grapefruit, and lemon, preferably using a microplane. You should have about 1 generous tablespoon total of zest. Use your fingertips to mix it into the salt mixture.
Preheat the oven to 400°F (204°C).
Beat the egg whites until they're just beginning to hold their shape, then fold them into the salt mixture.
Line a 9-inch square baking dish with parchment paper or aluminum foil. Pour enough of the salt mixture into the dish to create a 1-inch-thick bed. Arrange the potatoes on the salt in a single layer. Cover with the remaining salt mixture. The potatoes should be completely encased with salt and spice.
Roast until the potatoes are tender, about 30 minutes for 1-inch potatoes or 35 minutes for 2-inch potatoes. Remove from the oven and let rest for 10 minutes.
For potatoes served whole, dump them in a bowl, toss with rosemary leaves, if desired, and drizzle with olive oil.For thin, chip-like potatoes, place the potatoes between pieces of parchment paper lightly brushed with oil and press a meat pounder or a heavy skillet against them to flatten. Heat a generous film of oil in a nonstick skillet over medium-high heat and sauté the potatoes on both sides to brown, about 2 1/2 minutes per side. Drain on the paper towels. Add some rosemary leaves to the oil and fry and crisp them for about 30 seconds. Arrange the potatoes on a plate and sprinkle with crunchy sea salt and rosemary. (The potatoes can be stored in olive oil in the fridge for up to 3 days.)