In medium saucepan, heat milk until it starts to bubble. Slowly add cornmeal, stirring continuously to ensure it is completely mixed. Switch heat to medium-high, and stir constantly for about 8 minutes, or until very thick. This mixture will be thick enough to hold your wooden spoon upright!
Remove saucepan from heat and add 1 tbsp butter, beaten eggs and salt. Beat until mixture is smooth. Spread into a greased 8x8 baking pan (at least 2" high sides) . Allow to cool in refrigerator for 2 hours, leaving uncovered.
Once cooled, cut into 2" squares (16 pieces total). Place in larger freezer container (about 10x6 size), ensuring edges aren't touching. Top each piece with a small amount of butter and then top with Parmesan cheese. Seal and freeze.