Preheat oven to 450° and line a baking sheet with parchment paper. Set aside.
In a small frying pan of medium high heat, add butter, or oil, and diced jalapenos. Cook until jalapenos become tender. Remove from heat and let cool for 5 minutes.
In a large bowl, whisk flour, sugar, baking powder, cream of tarter and salt together until combined.
Cut butter into flour mixture using a pastry blender or fork until crumbly.
Whisk 1 cup of buttermilk and egg together then add to dry ingredients and mix until almost fully combined until a dough forms.
Add shredded cheese and diced jalapenos to dough and using clean hands, knead dough until combined.
Place dough on a generously floured surface and knead until dough is smooth.
Using a rolling pin, roll dough out to ¼ inch thick.
Using a biscuit cutter or circular cookie cutter, cut out biscuits and place on prepared baking sheet.
Brush tops of biscuits with remaining ¼ cup of buttermilk.
Bake for 10-12 minutes or until slightly golden brown.
Serve hot with butter.