Preheat oven to 350 degrees.
In a medium bowl, mix flour, baking powder, salt, to taste, and sugar together using a fork; cut in shortening until it resembles cornmeal. Add cheese. Sir in buttermilk all at one time just until blended. Do not over stir.
Drop by tablespoonfuls, or use an ice cream scoop, onto a well-greased baking sheet. Brush dough with melted butter. Bake for 12 to 15 minutes.
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