In a large nonstick skillet, combine the sugar, lemon juice and lemon zest. Cook over moderate heat, stirring occasionally, until the sugar turns golden brown, about 7 minutes. Add the shallots and radishes. Stir in 1 tablespoon of the butter, the cardamom and 1 1/2 cups of water and season with 1 1/4 teaspoons coarse salt and 1/4 teaspoon pepper. Cover and cook over moderate heat for 5 minutes, tossing frequently. Uncover and boil over moderately high heat until the vegetables are crisp-tender and glazed, about 7 minutes. Transfer to a bowl.