In a large bowl, combine the water and lemon juice; set aside. Cut off the base of each artichoke. Snap off outer leaves until you reach leaves that are yellow at the bottom. Cut off the top third of artichokes; quarter artichokes. Immediately place artichokes in water mixture to keep them from browning. Drain artichokes.
Meanwhile, preheat oven to 350 degrees F. Cook noodles according to package directions; drain. Rinse with cold water; drain again. In a large saucepan, heat 2 tablespoons of the oil over medium heat. Add artichokes, pine nuts, and half of the garlic. Cook for 8 to 10 minutes or until artichokes are tender, stirring frequently. Transfer to the large bowl. Stir in ricotta cheese, 1/2 cup of the Parmesan cheese, 1/2 cup of the basil, the egg, and salt.
In a small bowl or glass measure, combine broth and flour. In the large saucepan, heat the remaining 1 tablespoon oil over medium heat. Add the remaining garlic; cook and stir until garlic is tender but not brown. Stir in flour mixture and half-and-half. Cook and stir until mixture is thickened and bubbly. Remove from heat. Stir in the remaining 1/2 cup basil.
In a small bowl, combine mozzarella cheese and the remaining 1/2 cup Parmesan cheese.
To assemble, spread about 1 cup of the sauce over the bottom of an ungreased 3-quart shallow baking dish. Layer three of the cooked noodles in the dish. Spread with one-third of the artichoke mixture and one-third of the remaining sauce. Sprinkle with 1/2 cup of the mozzarella mixture. Repeat layering noodles, artichoke mixture, sauce, and mozzarella mixture two more times.
Bake, uncovered, for 35 to 40 minutes until edges are bubbly and top is lightly browned. Let stand for 15 minutes before serving. Makes 12 servings.