In a food processor, combine the grated sharp cheddar cheese, all-purpose flour, and cold unsalted butter. Pulse until the mixture resembles coarse crumbs, which should take about 30 seconds.

Gently add the plain yogurt to the crumb mixture. Pulse again until the mixture is crumbly yet holds together when squeezed—this should take about 15-20 seconds.

Shape the mixture into logs, wrap them tightly in plastic wrap, and refrigerate for at least 30 minutes.

Preheat your oven to 350°F (175°C). Roll the chilled dough out on a lightly floured surface to about 1/8-1/4 inch thickness.

Using a pizza cutter or a fluted pastry wheel, slice the rolled dough into 1-inch squares and poke holes in each square with a skewer.

Place the cut crackers onto a baking sheet lined with parchment paper and bake for 17-20 minutes until golden brown.