Use a medium-size mixing bowl to combine the flour, salt, cream of tartar, baking powder, and baking soda. Stir them all up together. Cut in the salted butter just as you would for pie crust dough.
Stir in the 1 cup of shredded cheddar cheese and the drained, chopped green chilies. Mix everything up thoroughly.
Add the beaten eggs and the sour cream, in that order. Mix everything all up together.
Add the milk and stir until everything is thoroughly combined.
Drop the biscuits by Tablespoonfuls onto ungreased baking sheets, 12 biscuits to a sheet.
Once the biscuits are on the baking sheet (or sheets if you decided to use two) you can wet your fingers with a little water and shape them if you like. (I leave mine slightly irregular so everyone knows they're homemade.)
Sprinkle the tops of the biscuits with the 1/2 cup of shredded cheese.
Bake the biscuits at 425 degrees F. for 12-14 minutes, or until they’re golden brown on top. For 2 sheets of smaller biscuits, reduce the baking time to 10-12 minutes. They’re done when they’re golden brown on top.
Cool the biscuits for at least five minutes on the cookie sheet, and then remove them to a wire rack. Let them cool for at least another 2 minutes before you serve them. (I place mine in a towel-lined basket so they stay warm.)
Yield: Makes 12 large Cheese And Green Chiles Biscuits, or 18 to 24 smaller biscuits that are equally delicious.