Combine the flour, baking powder, salt, and grated butter in a large bowl. Using your fingers, press the butter into the flour until a coarse mixture forms (it will look like wet sand).
Add in the cold milk and stir until a dough forms. Gently fold in the cheddar cheese, green chiles, paprika, and garlic powder.
Turn the dough onto a lightly floured surface and pat it into a 10 x 10 square leaving it about 1/2 inch to 3/4 of an inch high. Using a biscuit cutter, cut out 5 or 6 biscuits and place on a greased baking sheet.
Gently gather the biscuit scraps together and pat into a square that is 3/4 inch high. Cut out more biscuits. Continue doing this until you have between 10-12 biscuits.
Bake the biscuits for 8-10 minutes or until they are beginning to brown.