Don't be deterred by all of the steps and ingredients here! (Seriously, come back. We have sandwiches.) Every component of this sandwich can be prepared a day or two (or more) ahead of time, which makes it perfect for a party, or a big messy lunch with friends.
As for the pickles, use whatever in-season vegetables you like, but the beets are pretty key to the DNA of this sandwich. In the summer, Caroline Fidanza -- the recipe's author -- uses fresh tomatoes and basil; in winter, it's roasted roots and chiffonaded kale. Go crazy.
Note: To make these sandwiches a little easier, you can buy store-bought pickled vegetables; ideally, I'd go with something local, that you know has been pickled with care. And look for beets. If you're feeling brave, though, read on; making them at home is worth it.
For the beet + onion pickles: Preheat the oven to 400° F. Put the beets in a roasting pan, add just enough water to the pan to evenly cover the bottom. Salt the beets with 1 tablespoon of salt and drizzle them with olive oil. Cover with foil and roast for about an hour, until they're tender when pierced with a knife. Let them cool, then peel the beets -- I like to use the foil, but you can also use your fingers or a paring knife. Cut them into 1/4-inch slices and put them in a large heatproof bowl with the sliced onions.
In a saucepan, combine the red wine vinegar, water, sugar, and 1/2 tablespoon kosher salt, plus the peppercorns, coriander seeds, mustard, anise, and allspice. Bring to a boil over medium-high heat, stirring to dissolve the sugar and salt. Pour the brine over the beets and onions, then let them cool at room temperature. Transfer them to a plastic or glass container, cover them, and refrigerate for at least a day. They'll last up to 2 months.
To make the carrot pickles: Place the sliced carrots in a heatproof bowl. In a saucepan, combine the apple cider vinegar, water, sugar, kosher salt, coriander, fennel, and the chiles. Boil, stir, and pour over the carrots. Cool them, then store in the fridge for at least a day, and up to 2 months.
When you're ready to make your sandwiches, grab about a cup of carrot pickles, and about 2 cups of the beet-onion pickles. Flick off any spices that cling, then thinly slice the beets and carrots. Toss your pickles with the herbs, radishes, capers, and olives, and add a drizzle of oil to hold everything together.
To assemble the sandwiches:
Boil your eggs: Boil water, then add the eggs and boil for 10 minutes. Transfer immediately to an ice bath, let them cool, then peel them and slice them thinly.
Slice your feta, if you can. Then assemble your sandwiches! Slice the focaccia into sandwich-sized pieces. For each sandwich, smear one slice of bread with about a tablespoon of aioli, then layer on a sliced egg and a slice of feta. Top with a handful of that beautiful salad. Cover it all with the second piece of bread, and serve immediately, with glee.