Preheat oven to 350°. Spray a 9x9" baking dish with cooking spray. Set aside.
Cut cabbage in coarse pieces, approximately 8 cups. Add sugar to a large pot of water, bring to a boil, and cook cabbage in boiling water 3 - 4 minutes. Drain well.
In a saucepan, combine mushroom soup (I use the low-sodium type), mayonnaise, milk and salt. Stir over low heat until blended and warm.
Spread ONE cup of the cornflakes in bottom of 9x9" baking dish. Layer half of cabbage, half of sauce, and half of cheese. Repeat layers, by starting with the second cup of cornflakes, then the rest of the cabbage, the rest of the sauce, and finishing with the remaining cheese on top.
Bake approximately 25 minutes in preheated oven, until cheese is bubbly and slightly browned.