With a strong, sharp knife or cleaver, cut through husk, corn and cob of each ear of corn, removing about 1/4" of corn on both ends of each ear.
Peel off husks without tearing them; rinse. To keep moist, place in plastic bags and seal; set aside. Pull silk from corn and discard; rinse corn.
With a knife or a corn scraper, cut the kernels from cobs; you will need 3 cups, lightly packed. Whirl in a food processor until finely ground. In a large mixer bowl, With a wooden spoon, mix together processed corn, masa harina, and warm water. Cover and let set for 20 minutes (masa will appear dry). Fit a paddle attachment on mixer. Beat shortening and sugar, into masa on medium speed for 1 minute. Scrape down sides of mixing bowl with rubber spatula. Continue mixing until masa resembles a thick creamy paste. Add salt, to taste. mix just to combine.
To shape each tamal, Holding the husk with the widest part away from you, place 2 Tbsp. masa in the center of the husk and spread outwards, leaving 2" at the bottom, and within 1/2" from the top, without masa. Add 1 Tbsp. cheese and 1 tsp. green chile in the center. Tri-fold the husk sides,over the masa. and fold up the bottom.
In a large steamer pot, with a rack that's 1" above boiling water, stand tamales upright folded end down. Support them against other tamales so ends stay shut. You can fill pan to capacity with tamales, stacking, but they need to be loose fitted into steamer so heat can circulate. Steam until tamales in center are firm to touch, not runny (pull a tamal out and open to test). about 1 hour. Add boiling water to pan as required to maintain water level.
Serve tamales hot; you can keep them warm over hot water for several hours. To freeze, let cool completely, then place in a single layer on baking sheets; When frozen solid, transfer to plastic bags and store in freezer for up to 6 months. To reheat, let thaw; then steam above boiling water until heated through, about 15 minutes.