In a large mixing bowl, whisk together the flour and salt until evenly distributed. Cut the cold, cubed butter into the flour mixture using a pastry cutter or two forks until the texture becomes crumbly and dry. Incorporate the beaten egg into the dough, stirring until just combined. Add the grated cheese and minced jalapeños, folding gently to evenly disperse throughout the mixture. Shape the dough into a ball, wrap it tightly in plastic wrap, and refrigerate for 1 hour to firm up. Preheat the oven to 400°F. Roll the chilled dough into 1-inch balls and arrange them on a baking sheet that has been either greased or lined with parchment paper, spacing them 2 inches apart. Press down on each dough ball with the flat bottom of a mug or jar to slightly flatten. Bake in the preheated oven for 14 to 18 minutes, or until the edges of the shortbreads begin to turn a light golden brown. Let them rest on the baking sheet for 5 minutes post-baking before transferring to a wire rack to cool completely.