Preheat oven to 400 degrees, and line baking sheet with parchment paper
Whisk the flour and baking powder together
Rub shortening into the flour mixture until it resembles course crumbs
Dissolve the sugar and salt into the beaten eggs and milk, whisking until sugar is dissolved
Add liquid to flour mixture all at once, and using a wooden spoon or spatula mix only until the mixture comes together. Dough will be sticky and wet.
Turn the dough out onto a well floured and surface and sprinkle with the shredded cheese. Work dough gently until dry and cheese is combined. Add flour as needed. Do not overwork the dough.
Knead 8 to 10 times and then sit aside to allow to rest for 5 to 10 minutes.
Roll out on a floured surface to about 2 cm thickness. Cut into 12 circles with a 3" biscuit cutter, place on parchment lined baking sheet
Brush with milk and bake for 12 to 15 minutes or until golden. Remove from oven and cool on a wire rack.
Notes
Store in an airtight container at room temperature for up to 3 days.