How to Make It
Working with 1 large artichoke at a time, cut off all but 2 inches of the leaves. Discard the dark outer leaves, then trim the artichoke bottom and stem. Quarter the bottom and scrape out the hairy choke. Rub the quarters with 1 lemon half, then squeeze the juice from the half into a bowl of water. Add the artichoke quarters. Repeat with the remaining large artichokes and lemon half.
In a saucepan, combine the lemon slices, garlic, red pepper and white wine with 1/2 cup each of oil, mint and water. Arrange the artichoke quarters in the saucepan; season with salt and pepper. Bring to a boil, cover and simmer over moderately low heat until the artichokes are just tender, 25 minutes. Let cool to room temperature.
In a small bowl, toss the red onion with 2 tablespoons of the lemon juice; let stand for 10 minutes. In another bowl, whisk the remaining 2 tablespoons each of oil and lemon juice with the citrus zests.
Remove the dark outer leaves from the baby artichokes and trim the stems. Using a mandoline, thinly shave the artichokes and toss with the lemon dressing. Drain the onion and add to the shaved artichokes with the remaining mint. Season with salt and pepper.
Arrange the bresaola on a platter. Using a slotted spoon, spread the cooked artichokes on the bresaola. Top with the shaved artichoke salad and a drizzle of olive oil and serve.