Remove stems and any bruised leaves from the greens. Wash thoroughly in cold water; drain well. Chop the leaves into rough, wide ribbons (should have about 6 cups packed greens).
In a Dutch oven, cook the greens, covered, in salted boiling water for 4 minutes. Add the turnips; cook for 6 to 8 minutes longer or until the greens are tender but still bright-colored and turnips are tender. Add the pearl onions; return to a boil just to thaw the onions. Drain well in a colander; set aside.
In a large saucepan melt the 3 Tbsp. butter. Stir in the flour, salt, pepper, and nutmeg. Add half-and-half all at once. Cook and stir over medium heat until thickened and bubbly. Remove from heat. Add shredded cheese, stirring until melted. Gently stir in the cooked greens mixture, then transfer to a 2-quart baking dish.
In a small bowl stir together the bread crumbs and the 2 Tbsp. melted butter. Sprinkle over the turnip mixture. Bake in a preheated 375-degree oven for 20 minutes or until bubbly and crumbs are golden brown.