In a large heavy saucepan, bring 6 cups water to a boil. Add 2 teaspoons salt, gradually whisk in cornmeal. Reduce heat to low.
Cook until mixture thickens and cornmeal is tender, about 15 minutes, stirring often.
Turn off heat, add butter. Stir until butter melts. Stir in chopped green onions.
Lightly butter a 13 x 9 inch baking dish, pour polenta into prepared dish, spread into a 1/2 inch thick layer, spreading it out as evenly as you can. Cool completely. Refrigerate 2 hours or until set. Using a 1 to 1 1/2 inch round cookie/biscuit cutter or shape of your choice, cut out rounds. (as many as you can) Continue with pan frying directions above.