Cut off pointy tops of artichokes to within 1 or 1 1/2 inches of the base. Remove all but about 1/2-inch of the stem. Cut all around the artichoke, removing all of the hard parts. Open up the center and dig out the choke with a blunt-edged spoon. Trim any remaining hard parts; what's left is the artichoke bottom. Heat 1/4 cup oil in a deep, large skillet over medium-high heat. Add onion and saute until it begins to soften, about 2 to 3 minutes. Lay the artichoke bottoms on top of the onion, then pour in the wine. Bring to a boil, reduce heat to low, and cover. Simmer, turning the artichokes after 15 minutes, until the bottoms are tender but not mushy, 30 to 45 minutes total. Remove cooked artichokes, reserving about 3/4 cup of the cooking liquid. Cut artichokes into bite-sized chunks and return them to the pan with the cooking liquid, add remaining 1 tablespoon oil, salt and pepper, to taste, and the lemon juice. Turn the heat to very low to keep them warm. Season the shrimp with salt and a tiny sprinkling of cayenne. Heat a large nonstick skillet over medium-high heat for 1 minute. Add the butter to the hot skillet. Dredge each of the shrimp in the orange dust and place them in the skillet. Cook until lightly browned, about 2 minutes, and then turn over and cook another 2 to 3 minutes. Divide the arugula among 4 plates. Top each with a portion of the artichokes and 6 shrimp; pour the artichoke liquid over all and garnish with basil. Sprinkle a little orange dust around the outside of each plate, and serve immediately.
Preheat oven to 350 degrees F. Use a vegetable peeler to peel the oranges; you should get 8 to 10 broad strips from each one. Scrape all the white pith from inside the peel using a paring knife. Place the peels in a small saucepan with 1 cup water and the sugar. Bring to a boil over high heat, reduce heat to medium and simmer 10 to 15 minutes or until the liquid becomes syrupy. Remove the peels and drain. Line a cookie sheet with aluminum foil and spread with the oil. Scatter the cooked peels on the foil; they should not touch one another. Bake until dry but not at all brown, about 15 minutes. If they begin to brown before they are dry, reduce oven temperature. Let cool at room temperature, preferably in a dry place. Crumble, then grind in a spice mill or coffee grinder until powdery. Store in a tightly sealed jar. Orange dust retains peak flavor for a couple of weeks, but it will keep virtually forever, gradually losing its intensity. Yield: about 3 tablespoons