Preheat oven to 400 degrees. Sift together flours, baking powder, baking soda, salt, and sugar. Repeat. Using a pastry cutter, cut in butter and shortening until mixture resembles coarse meal. Make a well in center, and add buttermilk. Stir until dough holds together.

Turn dough onto a generously floured surface. Fold dough over on itself 3 or 4 times. Pat to 1 inch thick. Cut out rounds with a floured 3-inch biscuit cutter. Place rounds 2 inches apart on a parchment-lined baking sheet. Gather scraps, and repeat. Brush tops with melted butter.

Bake until golden brown, 15 to 18 minutes. Serve warm, or let cool completely and store in an airtight container at room temperature for up to 3 days.

Heat a large skillet over medium-high heat. Add sausage and cook, turning occasionally and breaking into small pieces with a wooden spoon, until browned, about 10 minutes.

Using a slotted spoon, transfer sausage to a bowl. Reserve about 3 tablespoons pan drippings in skillet, and pour off remaining drippings. Add flour, and cook over medium heat, stirring, for 4 minutes. Stir in evaporated milk, stock, and half-and-half. Bring to a simmer, stirring and scraping bottom of skillet constantly, and cook until thickened, about 8 minutes. Stir in nutmeg, cayenne, salt, pepper, and reserved sausage.

Heat 1 tablespoon oil or butter in a large skillet over medium-high heat. Crack 4 eggs into skillet, and cook, uncovered, until whites are set, about 2 minutes (if you prefer to cook your yolks further, cover skillet).

Transfer to a plate. Repeat. Arrange 1 or 2 biscuits on each plate. Top with gravy. Place 1 egg on each biscuit. Season with salt, pepper, and hot sauce.