Heat oven to 425°F (220°C). Cube butter and freeze for 10 minutes. Line a baking sheet with parchment.
Whisk flour, baking powder, baking soda, and salt in a large bowl. Add cold butter and press each piece flat between your fingers until the mixture is shaggy with pea- to almond-sized butter pieces throughout.
Add cold buttermilk and stir with a fork until a rough dough barely holds together. Turn onto a floured surface, pat to 1 inch thick, fold in thirds, pat again. Repeat the fold once more, then pat to 3/4 inch and cut into rounds with a sharp-edged cutter without twisting.
Place biscuits on the sheet with sides touching. Brush tops with buttermilk. Bake 12 to 15 minutes until light golden and puffed.
While biscuits bake, cook sausage in a cast iron skillet over medium-high heat for 7 to 9 minutes, breaking into crumbles, until browned with dark edges. Cook ground beef to 160°F internal temperature. Do not drain the fat.
Reduce heat to medium. Add flour to the pan and stir for 2 minutes. Pour in warmed milk in a slow stream while whisking. Cook 4 to 6 minutes, stirring, until the gravy coats a spoon heavily.
Season with black pepper, cayenne if using, and salt. Split biscuits, ladle gravy over both halves, and serve immediately.
