1. Preheat oven to 400°.
2. Combine 1 cup water and juice in a bowl. Cut artichoke tops off; trim stems. Quarter artichokes; place in bowl. Combine 2 cups water and wine in a saucepan. Place peppercorns in center of cheesecloth; tie ends. Add sachet to pan; bring to a simmer. Drain artichokes; add to pot. Simmer 5 minutes; drain. Discard sachet. Heat a small skillet over medium-high heat. Coat pan with cooking spray. Add shallots; sauté 5 minutes. Combine shallots, artichokes, and radishes.
3. Roll dough out to a 15-inch circle; rub with garlic. Place dough on a baking sheet. Sprinkle with nuts and cheese, leaving a 2-inch border. Top with artichoke mixture, thyme, pepper, and salt. Fold edges of dough over to partially cover. Bake at 400° for 30 minutes or until browned.