Combine the flour, 4 tablespoons of the sugar (reserve remaining tablespoon to sprinkle onto the shortcakes), the baking powder, and salt in a medium bowl
Add the chilled butter and cut it in with a pastry blender (or work it into the flour mixture using your fingertips) until the particles are very fine.
Force the egg yolks through a fine sieve and stir them into the flour mixture. If you wish, you can use the food processor to cut the butter into the flour until the mixture is very fine; add the egg yolks and pulse them in until very fine. If using the food processor, transfer the mixture to a medium bowl.
Add 3/4 cup of heavy cream and stir gently with a fork until the dough is moistened and just holds together. It should be a fairly stiff dough. If it seems too dry, add more cream a little at a time, and stir until the dough just gathers together.
Scrape the dough onto a lightly floured work surface and dust all surfaces lightly with flour. Knead gently 3 or 4 times and pat the dough to a scant 3/4-inch thickness.
With a floured 3-inch plain round cutter, cut out 4 biscuits and place them 2 inches apart on a heavy baking sheet.
Gather the scraps and reform them as gently as possible into a smooth mass.
Pat the dough out again and cut 2 more biscuits. Place them on the baking sheet.
Place them on the baking sheet. The shortcakes may be baked hours before serving.
Adjust an oven rack to the center position and preheat the oven to 375 degrees.
Brush the tops of the biscuits lightly with the 1 tablespoon melted butter and sprinkle them with the remaining 1 tablespoon sugar.
Bake about 15 minutes, or until the biscuits are golden brown and cooked through. A toothpick inserted into the center of a biscuit should come out clean.
Let the biscuits stand until cool.