Special equipment: a mandolin slicer, optional; a deep fryer, optional
In a shallow Dutch oven or braising pan, heat the olive oil over medium heat. Add the shallots and garlic and cook, stirring occasionally, until soft but not browned, about 5 minutes. Add the olives, white wine and capers and cook about 2 minutes.
Halve 6 of the cleaned artichokes and place them in the braising liquid. Add the tomatoes and their liquid and season with salt and pepper. Be sure to taste, as the olives and capers can make the sauce very salty. Cover the mixture, bring to a simmer and cook over medium heat until the artichokes are tender (a knife should go through without resistance) and the liquid has reduced by half, about 40 minutes.
Preheat the oven to 375 degrees F. Drop dollops of the ricotta cheese on each artichoke, then top with the grated Pecorino. Bake in the oven covered for 20 minutes. Uncover and bake until golden brown, about 25 minutes.
In the meantime, heat 2 inches canola oil in a Dutch oven or fryer to 350 degrees F. Slice the remaining 2 artichokes extremely thin using a mandolin slicer or by hand. Pat the slices dry with paper towels. Drop the artichoke slices into the hot oil and fry until golden brown and crispy, about 5 minutes.
Top the baked artichoke with the fried artichoke slices and tarragon serve.
This recipe has been updated and may differ from what was originally published or broadcast.