Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, cream the softened butter until smooth.
Gradually add the flour, cornstarch, salt, garlic powder (if using), and paprika (if using), mixing until combined.
Stir in the grated cheddar cheese and chopped jalapeños, blending until evenly distributed throughout the dough.
Shape the dough into a disc, cover it with plastic wrap, and refrigerate for at least 30 minutes to firm up the dough.
After chilling, roll out the dough on a lightly floured surface to about ¼ inch thick.
Use a cookie cutter or a knife to cut the dough into your desired shapes (rounds, squares, or even wedges).
Place the shaped cookies on the prepared baking sheet, spacing them about 1 inch apart.
Bake for 20-25 minutes, or until the edges are golden brown and the cookies are crisp.
Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.