Pulse together the cream cheese, the 2/3 cup softened butter, and 1 cup of the flour two or three times in a food processor fitted with the knife or dough blade. Turn the dough out onto waxed paper and divide into two rounds. Wrap in waxed paper, plastic wrap, or a resealable plastic bag, and refrigerate for at least 30 minutes.
When ready to bake, preheat oven to 425 degrees F.
Lightly sprinkle a board or other clean surface with some of the remaining flour. Sprinkle the top lightly with flour. With floured hands and a floured rolling pin, roll out one portion of the dough at a time to approximately 1/2-inch thick. For each biscuit, dip a 1- to 1 1/4-inch biscuit cutter into the remaining flour and cut out the biscuits, starting at the outside edge and cutting very close together, being careful not to twist the cutter. The scraps may be combined to make additional biscuits, although these scraps make tougher biscuits.
Using a metal spatula if necessary, move the biscuits to an ungreased baking sheet, placing the biscuits 1 inch apart. Bake the biscuits on the top rack of the oven for a total of 10 to 12 minutes until light golden brown. After 6 minutes, rotate the pan in the oven so that the front of the pan is now turned to the back, and check to see if the bottoms are browning too quickly. If so, slide another baking pan underneath to add insulation and retard browning. Continue baking another 4 to 6 minutes until the biscuits are light golden brown. When the biscuits are done, lightly brush the tops with the 1/3 cup softened or melted butter. Turn the biscuits out upside down on a plate to cool slightly. Serve hot, right side up.
These biscuits may be frozen, unbaked or baked, and reheated.
Sift together 1 cup all-purpose flour (or 1/2 cup cake flour with 1/2 cup all-purpose flour), 1/2 to 1 teaspoon salt, and 1 1/2 teaspoons baking powder.
Variation: Press a small spoon into the center of each dough round and insert a 1/4 teaspoon of Hot Pepper Jelly before or after baking.