Prepare Dry Mix: In a medium bowl, sift together the flour, dry mustard, salt, and cayenne pepper. This ensures the spices are evenly distributed and helps create a light, tender dough. Set this mixture aside while you prepare the wet ingredients.
Cream Cheese and Butter: Using a stand mixer fitted with the paddle attachment, combine the grated cheddar cheese and softened butter. Mix on medium speed until the mixture is smooth and spreadable, about 2 minutes. This step is essential for ensuring the cheese and butter meld thoroughly, providing a rich flavor base.
Incorporate Dry Ingredients: Reduce the mixer speed to low. Gradually add the flour and spice mixture to the cheese and butter blend, mixing until fully combined. Then add 2 tablespoons of cold water and continue mixing on medium speed for about one minute, until the dough forms a cohesive ball.
Shape the Dough: Turn the dough onto a lightly floured surface. Knead gently about five times to bring the dough together, taking care not to overwork it. Place the dough on a large sheet of parchment or wax paper and roll it out into a 12-by-9-inch rectangle, approximately 1/4 inch thick. Transfer the dough with the paper onto a baking sheet and chill in the refrigerator for at least 15 minutes to firm up.
Slice into Strips: Preheat your oven to 425°F (220°C). Line two baking sheets with parchment paper. Remove the chilled dough from the fridge and cut it in half crosswise. Then slice each half into strips approximately 1/4 inch wide and 6 inches long. Arrange the strips on the prepared baking sheets, leaving at least half an inch between each strip.
Create Curves for Texture: Gently wiggle each dough strip with your fingertips on the baking sheet to form a slight, wavy shape. This not only adds visual appeal but also enhances the crispy texture.
Bake to Golden Crisp: Bake one sheet at a time in the preheated oven until the cheese straws turn a golden brown and become crisp, about 12 to 14 minutes. Remove from the oven and let cool on the baking sheets for 10 minutes.
Final Cooling: Transfer the cheese straws to a wire rack to cool completely, approximately 15 minutes. This step helps maintain their signature snap and prevents sogginess.