Preheat oven to 300°. Snap off leaves of artichokes down to the yellow-green layer. Trim green tips of remaining leaves and fibrous surface from stems.
Pour 1/4 cup oil into a small rimmed baking pan. Add artichokes, herbs, 4 tsp. zest, and 1/2 tsp. salt; turn to coat artichokes. Cover pan with foil and roast artichokes until tender when pierced with the tip of a knife, 30 to 45 minutes.
Uncover pan and set oven to broil. Broil artichokes, turning every minute or so, until browned all over, about 8 minutes. Transfer artichokes to a cutting board. Pour any oil from pan into a measuring cup and add enough extra oil to equal 1/2 cup; then pour into a large cast-iron or nonstick frying pan.
Make salsa: Heat artichoke oil over medium-high heat. Add fava beans and cook, stirring often, until favas are heated through, 3 to 4 minutes. Add chile flakes, garlic, and remaining lemon zest and cook 1 minute. Pour into a bowl and gently toss with lemon juice, almonds, dill, and salt to taste. Add extra oil to loosen if you like.
Cut some artichokes in half and divide, with whole artichokes, among 4 plates (or arrange on a platter). Spoon salsa over and around the artichokes and scatter olives here and there. Using a vegetable peeler, generously shave wide curls of parmesan over each plate. Top with miner's lettuce.
*To peel favas, shuck 1 lb. whole pods. Blanch beans 2 minutes in boiling water, dunk in cold water, and pop out of skins (slit skins with a knife or your fingernail); you should have about 1 cup.
Quick twist: Use fresh kiwi fruit (yes, kiwi!) instead of artichokes. Peel, slice, drizzle with extra-virgin olive oil, and sprinkle with sea salt and freshly ground black pepper. Skip the salsa. Top with miner's lettuce (or another mild, tender green such as mâche), shaved parmesan, and toasted chopped macadamia nuts.
Note: Nutritional analysis is per serving.