Preheat oven to 450 degrees F. Grease a 6.5 inch cast iron skillet or 2 3.5 inch skillets OR a small cake pan very thoroughly with butter. You can preheat the oven immediately if yours takes a while to get hot, or you can preheat while the flour mixture is getting cold.
Put your flour in a mixing bowl and add the softened 1/2 tablespoon butter and shortening. Mix it up with a spoon or heavy duty scraper, coating the flour particles the best you can until fat is evenly blended and mixture is crumbly. Place bowl in the freezer for about 20 minutes or just keep it there until you are ready to use it. The point is to get it really cold rather than frozen solid.
To your cold flour mixture, add all of the cream and stir until blended, then add buttermilk 1 tablespoon at a time until mixture resembles cottage cheese. It will be very lumpy and bumpy! You may need only 3 tablespoons, so go slowly with the milk and don't add it all at once.
Put the shaping flour (1/4 to 1/3 cup) in a shallow bowl next to your mixing bowl.
With your spoon or scraper, scoop up half of the soft biscuit dough and plop it in the extra flour. Dust top with the lightly, then shake off excess. Put it in the skillet. Repeat with remaining biscuit batter, setting the two biscuit dough sections side by side so they'll bake into each other.
Bake in upper third of oven for about 18 minutes, or until golden brown and puffed. Pull from oven and immediately brush with melted butter. Let rest for about 10 minutes before serving.