Whisk together the flour, sugar, baking powder, yeast, and salt in a large bowl. Cut in the shortening and 1/4 cup butter pats until pea-size bits remain. Add the milk and gently stir until combined. The dough will be wet.
Transfer the dough to a well-floured surface and gently pat into a 9-inch round that is 1-inch thick. Cut the dough into 2-inch rounds using a cookie cutter. Transfer the rounds to a parchment paper-lined baking sheet that has been lightly coated with cooking spray. Cover with a clean kitchen towel and let sit at room temperature for 1 hour. Remove the towel and cover with plastic wrap and place in the freezer for 1 hour and up to 24 hours.
Cook's Note: The longer the biscuits stay in the freezer, the lighter and fluffier they become. You can make ahead and just bake off a few as you need them.
Preheat the oven to 400 degrees F. Brush the tops of the biscuits with the heavy cream and bake until golden brown, about 15 minutes. Remove from the oven and brush the tops with the melted butter. Let cool slightly, then sprinkle the top with black pepper and slice open.
Heat 1 tablespoon of the unsalted butter in a small (6-inch) nonstick saute pan over medium-high heat until it begins to sizzle. Add one egg at a time, season top with salt and pepper and cook until the white is set, gently flip over and continue cooking for another minute or so. Flip so the top side is up. Place a few slices of ham on the bottom biscuit and top with the egg, place the other half of the biscuit on top and serve immediately.
Macerate the berries with the sugar in a bowl for about 30 minutes. Put some of the berries on the bottom half of the biscuit. Add whipped cream and top with the other half of the biscuit.