Combine flour and salt in a large bowl. Cut in butter using a pastry knife or two forks. Mixture will be dry and crumbly. Stir in beaten egg and then add cheese and jalapeño. Roll into a ball and cover with plastic wrap. Refrigerate for 1 hour.
Heat oven to 400°F. Roll dough into 1” balls and place on greased or lined baking sheet spaced 2” apart. Press each cookie to flatten slightly using a flat-bottomed mug or jar.
Bake for 14-18 minutes or until shortbread is just beginning to turn golden brown. Allow to cool on pan for 5 minutes and then transfer to wire rack to cool completely before serving.