Cook artichokes: Fill a 6- to 8-qt. pot half full of water and add aromatics. Season water with salt, then add oil, vinegar, peppercorns, and wine; squeeze in lemon, and drop in peel. Bring to a boil, then, lower heat to a bare simmer.
Cut off spiny tops of artichokes, snap off dark green outer leaves down to tender yellowish ones, and trim fibrous outer layer of stem. Cut artichokes in half lengthwise; if they have a fuzzy choke, scoop it out with a small spoon. Add artichokes to pot (they should be submerged; add more water if needed), and simmer, partly covered, until they offer very little resistance when pierced with a knife, 15 to 18 minutes.Let artichokes cool, uncovered, in cooking liquid (to absorb more flavor and firm up).
Meanwhile, make vinaigrette: In a small bowl, whisk lemon juice and shallot with salt. Let sit at least 5 minutes to soften the shallot’s bite and infuse oil with flavor, then whisk in pepper to taste and the oil. Season with more salt and pepper if you like.
Prepare everything else: Put potatoes in a medium saucepan and cover with cold water. Season water with fine salt. Bring to a boil, then lower heat and simmer until potatoes offer no resistance when pierced with a knife, 15 to 20 minutes. Transfer to a plate (save water in pot).
Season shelled favas with 1 tbsp. vinaigrette; chill.
Return potato water to a boil. Set a bowl of ice water near the stove. Cook eggs 7 minutes, adjusting heat to maintain a gentle boil. Cool eggs in ice water, then crack and peel.
Slice cooked potatoes crosswise into 1/2-in.-thick coins. Halve eggs lengthwise. Thinly slice fennel across top with a handheld slicer (or a knife), then toss with liquid and pat dry. Season with fine salt and drizzle with 1/4 cup vinaigrette.
Plate salads: Arrange arugula across bottoms of 2 large shallow bowls or platters. Top with groupings of artichokes, fava beans, potatoes, eggs, salami, and olives. Scatter a few herbs across favas and artichokes. Season potatoes and eggs with flaky salt and black pepper or piment d’Espelette. Drizzle salads with another 1/4 cup or so of vinaigrette and top with chive blossoms, if using, and flaky sea salt. Serve with remaining vinaigrette.
*To prep favas, boil beans 1 minute, then cool in a bowl of ice water before draining. Tear skins at one end and pop out inner beans into a bowl. Find ground piment d’Espelette, a flavorful Basque chile, on ($10.99 for a 15-gram jar).
MAKE AHEAD: Artichokes in cooking liquid, vinaigrette, potatoes, and unpeeled eggs, up to 4 days, chilled airtight. Peeled favas, up to 4 hours, chilled.