Position an oven rack in the center and preheat the oven to 350°F (175°C). Generously flour a clean work surface or a large piece of parchment paper. Place one disc of dough in the center and gently pat it into a rough 5-by-6-inch rectangle.
Dust the top of the dough with additional flour, flip, and repeat dusting. Using a rolling pin, roll out the dough evenly from the center outward, lightly dusting with more flour as needed to prevent sticking. Aim for a sheet roughly 15-by-11 inches in size and about 1/8 inch thick.
Carefully slide the parchment and dough onto a baking sheet. Brush off any excess flour from the surface. Repeat the process with the second disc of dough.
For a traditional store-bought appearance, score the dough into twelve 2 1/4-by-4 3/4-inch rectangles. Dock each rectangle with a bamboo skewer or the thin end of a chopstick to create the signature perforations. Alternatively, leave the dough whole for a more rustic presentation.
Bake the sheets in the preheated oven for 10 to 12 minutes, or until the crackers are firm to the touch and develop a rich, golden-brown hue.
Immediately after baking, while still warm, cut along the scored lines with a sharp knife or use a pizza wheel to craft free-form shapes. Allow the crackers to cool completely on the baking sheets before transferring.
Store the graham crackers in an airtight container at room temperature for up to 3 weeks, or freeze for up to 3 months for extended freshness.