Preheat your oven to 350°F (175°C) and place a sheet of parchment paper on a baking tray.
In a mixing bowl, whisk together the flour, salt, baking powder, paprika, and cayenne pepper.
Add the cold butter to the dry ingredients and cut it in using a pastry cutter or fork until the mixture resembles coarse crumbs.
Stir in the grated cheddar cheese.
Gradually add the ice water and cold milk, mixing until the dough comes together.
Flatten the dough on a surface dusted with a bit of flour until it's approximately 1/4 inch thick.
Cut the dough into thin strips or desired shapes.
Place the strips on the prepared baking sheet and bake for 12-15 minutes or until golden and crispy.
Allow the cheese straws to cool before serving.