In the bowl of a food processor, combine the flour, grated cheddar cheese, and cold butter cubes. Pulse the mixture several times until it transforms into coarse, crumb-like crumbs.

Add the yogurt and pulse again, blending until the dough begins to come together. It will still appear somewhat crumbly but should hold when pressed between your fingers.

Turn the dough out onto a clean surface and form it into a compact log shape. Wrap tightly in plastic wrap and refrigerate for a minimum of 30 minutes. Chilling ensures the dough firms up, making it far easier to roll out and cut. If the dough has been chilled for an extended period, allow it to rest at room temperature for a few minutes before handling.

Preheat your oven to 350°F (175°C). Prepare your work surface by laying down a sheet of parchment paper and dusting it lightly with flour. Place the chilled dough in the center and roll it out evenly, working from the center outwards and rotating the dough occasionally to maintain an even thickness of about 1/8 to 1/4 inch.

Using a pizza cutter or a fluted pastry wheel, slice the dough into one-inch squares. Trim the edges if needed to achieve uniform shapes. Carefully transfer the parchment paper with the cut squares onto a baking sheet, spacing the crackers slightly apart to prevent sticking during baking.

With the tip of a skewer or chopstick, pierce a small hole in the center of each cracker to allow steam to escape and ensure an even bake.

Bake in the preheated oven for 17–20 minutes or until the crackers are puffed and lightly golden. Remove from the oven and allow to cool completely on a wire rack before serving. Enjoy the crisp, cheesy goodness as a delightful snack!