1. Combine 4 cups water and juice. Cut off stem of each artichoke to within 1 inch of base; peel stem. Remove bottom leaves and tough outer leaves, leaving tender heart and bottom. Cut each artichoke in half lengthwise. Remove fuzzy thistle from bottom with a spoon. Thinly slice each artichoke heart; place in lemon water. Drain.
2. Heat 2 tablespoons oil in a large skillet over medium heat. Add garlic to pan; cook 1 minute. Add artichokes and 1/4 teaspoon salt; cover and cook 10 minutes or until artichokes are tender, stirring occasionally.
3. Cook pasta according to package instructions, omitting salt and fat. Drain pasta in a colander over a bowl, reserving 1/2 cup cooking liquid. Combine remaining 1 tablespoon oil, remaining 1/2 teaspoon salt, artichoke mixture, pasta, reserved cooking liquid, parsley, and pepper in a large bowl, tossing to combine. Add ricotta in spoonfuls, stirring gently to combine. Spoon 1 1/3 cups pasta mixture into each of 6 bowls; top each serving with 2 tablespoons Parmigiano-Reggiano.