1 1/2 pounds medium brussels sprouts, trimmed and bottoms scored with an "x"
1/4 cup sugar
1/3 cup fresh lemon juice
1 tablespoon finely grated lemon zest
1 pound medium shallots, peeled
1 pound medium radishes, 1/4 inch of the green tops left on
3 tablespoons unsalted butter
1/4 teaspoon ground cardamom
Coarse salt and freshly ground pepper
Bring a large saucepan of salted water to a boil. Add the brussels sprouts and cook over moderately high heat until crisp-tender, about 3 minutes. Plunge the sprouts into a bowl of ice water to cool, then drain.
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.
Melt the remaining 2 tablespoons butter in the skillet. Add the brussels sprouts and sauté over moderately high heat until lightly browned, about 5 minutes. Season with coarse salt and pepper. Add the glazed radishes and shallots and cook, tossing, until heated through, about 3 minutes. Transfer to a bowl and serve.
The recipe can be prepared through Step Two up to 1 day ahead; cover and refrigerate the glazed vegetables and the brussels sprouts separately. Let them return to room temperature before serving.