In the work bowl of a food processor, combine flour, salt, sugar, and poppy seeds. Pulse to combine. Add butter, and pulse until mixture is crumbly. With processor running, add half-and-half in a slow, steady stream just until dough comes together. Turn out dough, and shape into a disk. Wrap in plastic wrap, and refrigerate for at least 1 hour.

Preheat oven to 375°. Divide dough in half. On a silicone baking mat or sheet of parchment, roll one half of dough into a 15-inch rectangle. (Roll out dough as thinly as possible.) Using a pizza cutter, cut dough into 2- or 3-inch squares. Repeat with remaining dough.

Transfer silicone mats to baking sheets, and bake until crackers are crisp and golden brown, 12 to 15 minutes.