Pour boiling water over cabbage and let stand 5 minutes; drain thoroughly.
Heat the next three ingredients together, then stir in a smooth mixture of the butter and flour.
Whisk until thickened and smooth.
Fold in corned beef and cabbage.
Spread in a greased 8-inch bake dish, sprinkle with cheese and noodles.
Bake at 375F until bubbly, about 20 minutes.