Preheat oven to 450F. Line a large baking pan with parchment paper.
In a large skillet over medium high heat, brown the sausage. Remove with a slotted spoon to a bowl and place in the freezer for 10-15 minutes, until cold.
In a large bowl, combine the flour, sugar, salt, baking powder, and cream of tartar. Mix well.
Grate the cold butter directly into the flour mixture and toss just until combined.
In a small bowl, whisk the egg and milk together. Pour into the flour mixture and mix just until combined.
Add the cooled sausage, cheddar, and chopped rosemary to toss just until combined. If your kitchen is warmer, place in the freezer for 10 minutes.
Transfer out on a floured surface. Pat into a ½” rectangle, then slice in half to stack on top of each other. Press down into 1 ½” rectangle. Slice into 10-12 biscuits.
Evenly distribute on the prepared baking pan.
Brush with an egg wash to bake for 20-25 minutes, until deeply golden on top.
