Cube cabbage into roughly 1.5" squares for even cooking. Put in large stock pot and cover with water. Bring to a boil, then reduce to simmer for 15-20 minutes. You want the cabbage to be just fork tender. Drain in colander while preparing cheese cause.
To prepare the bechamel sauce;.
In the 2 cups of milk, whisk in well the 1/3 cup of flour. Melt the stick of butter, with salt, pepper, and garlic added, in a sauce pan on medium heat. Once the butter is melted, slowly whisk in the milk/flour mix. Continue to slowly whisk until sauce starts to thicken. You may need to turn heat up just a bit to get a gentle boil, then reduce back down to simmer. Once you think the sauce is thick enough, add 2 cups of shredded cheddar cheese and blend until melted. Turn off heat.
Put drained cabbage in a 9"x11" baking dish (or large Corning French White style casserole dish.) No need to spray or coat pan, unless you use metal. Pour the bechamel sauce over cabbage, and gentle turn cabbage to coat. Sprinkle the last cup of cheddar cheese on the top. Bake for 30 minutes on 350.