In a skillet over medium-high heat, brown sausage until cooked through, breaking up the sausage into small pea-sized pieces as it cooks. Transfer to a paper towel-lined plate to drain.
Melt butter in skillet. Add flour and whisk until combined. Add milk a little at a time while whisking constantly until all milk is incorporated and gravy is smooth.
Season with salt and pepper to taste. Cook 1-2 minutes until gravy is thickened. Stir in sausage.
Chill in the freezer for about 15 minutes while you prepare the biscuits.
To make the biscuits:
Preheat oven to 400 degrees F. Line a sheet pan with parchment paper or grease lightly with butter.
Combine the butter, baking powder, baking soda, and salt in a large bowl. Add the cold cubed butter and use a fork or a pastry blender to cut the butter into the dry ingredients. Mixture will look very crumbly.
Add buttermilk and use a spoon and then your hands to bring it together. Dump the mixture out onto a clean surface and knead it a few times to incorporate any dry bits. (Mixture will look very dry after you add all the buttermilk milk and you may be tempted to add more, but if you work it with your hands for a bit, it'll come together.)
Lightly flour your surface and roll biscuits out to 1/2 inch thick.
Use a 3-inch round cutter to make 12 rounds. Place half of the biscuit rounds on the prepared pan and brush with egg wash.
With a spoon or small cookie scoop, scoop cold gravy onto the center of the biscuits on the pan. Gravy should hold its shape. If it's still too loose, freeze for a few more minutes.
Use your fingers to gently stretch the remaining biscuit rounds a bit. Brush with egg wash and place on top of the scooped gravy, egg wash-side down. Press biscuit rounds together, sealing the gravy inside.
Brush tops with more egg wash and bake until golden brown, 22-25 minutes. Serve immediately or cool and store well-wrapped in the fridge for up to 3 days and in the freezer for 1 month.
You may have leftover gravy. Spoon it over baked biscuits before serving, if desired.
To reheat from frozen, heat in the microwave on high for 2 minutes.