For the biscuit topping: In a large mixing bowl, whisk together the flour, baking powder, yeast, salt and baking soda. Add the butter and shortening or lard to the bowl and gently mix to coat the fat. Work the fat into the flour mixture by hand until the mixture resembles cornmeal and there are pea-size bits of fat throughout the dough.
Whisk together the buttermilk and maple syrup, then pour over the flour and fat mixture. Gently stir with a wooden spoon (or Danish dough whisk; see Cook's Note) to just combine, making sure there are no flour clumps left. Cover with plastic wrap and refrigerate for at least 2 hours.
For the casserole: Preheat the oven to 400 degrees F; spray a 3.5-quart low braising pan or deep skillet with nonstick cooking spray and line with the tater tots. Bake for 20 minutes.
In the meantime, in a large nonstick skillet set over medium-high heat, brown the sausage, about 7 minutes. Drain the fat and set the sausage aside. In the same skillet over medium heat, cook the eggs, stirring, until a soft scrambled consistency, then salt and pepper to taste.
Roll out the biscuit dough on a lightly floured surface into a 12-inch round. Score the dough in a sun pattern (just a slight score, don't cut all the way through).
Remove the pan from the oven and spread the sausage in an even layer over top of the tater tots, then spread the scrambled eggs over the sausage. Sprinkle evenly with the grated Cheddar. Top everything with the biscuit dough round.
Reduce the oven temperature to 375 degrees F and bake until the crust is deep golden brown, 35 to 40 minutes. Immediately brush with the melted butter. Let rest for 5 to 10 minutes before serving.
A Danish dough whisk is a flat, rigid whisk for mixing/blending various types of dough without overworking the dough or clogging. It can be found at cooking stores or online.