Preheat the oven to 425°F (220°C). Line a baking sheet with parchment paper.
In a large mixing bowl, whisk together the all-purpose flour, baking powder, granulated sugar, baking soda, and 1 teaspoon salt.
Add the cold, cubed unsalted butter to the flour mixture. Using a pastry cutter or your fingers, cut the butter into the flour until the mixture resembles coarse crumbs with pea-sized pieces of butter remaining.
Pour the cold buttermilk into the flour and butter mixture. Stir gently with a wooden spoon until the dough just comes together. Do not overmix.
Turn the dough out onto a lightly floured surface. Gently knead the dough 3 to 4 times until it holds together.
Pat the dough into a 1-inch thick rectangle. Using a 2.5-inch round biscuit cutter, cut out 6 biscuits. Place them on the prepared baking sheet, spacing them about 1 inch apart.
Gather the scraps, gently pat together, and cut out additional biscuits if desired.
Bake the biscuits for 12 to 15 minutes, or until golden brown on top. Remove from the oven and let cool on a wire rack.
While the biscuits bake, whisk together the eggs, whole milk, 1/2 teaspoon salt, and black pepper in a medium bowl.
Heat a nonstick skillet over medium heat and lightly grease with cooking spray or a small amount of butter.
Pour the egg mixture into the skillet and cook, stirring gently, until the eggs are softly scrambled and cooked through, about 3 to 4 minutes. Remove from heat.
To assemble each sandwich, slice a biscuit in half horizontally. Place one cooked turkey sausage patty on the bottom half, top with a slice of cheddar cheese, then add a portion of scrambled eggs. Cover with the biscuit top.
If freezing, wrap each sandwich tightly in plastic wrap and then place in a freezer-safe zip-top bag. Freeze for up to 2 months.
To reheat, unwrap the sandwich and microwave on high for 1 to 2 minutes or until heated through. Alternatively, reheat in a 350°F (175°C) oven wrapped in foil for 15 to 20 minutes.