In the bowl of a food processor, combine the butter, cheese, salt, flour, oregano, granulated garlic, and tomato paste and pulse until a crumbly dough forms. With the food processor running, drizzle in 1 tablespoon of water, adding the remaining tablespoon if needed until the dough just comes together.

Divide dough in half and wrap each in plastic wrap and flatten dough into discs. Refrigerate for an hour, until firm.

Preheat oven to 375°F. Line two rimmed baking sheets with parchment and set aside.

Working with one disc of dough at a time, roll out into a thin rectangle, about 1/8th of an inch thick. Transfer the dough to the parchment-lined sheets. Using a ruler of something with a straight edge and a pizza cutter or knife, cut rectangle into a grid of 2-inch squares.

Sprinkle lightly with salt and more oregano. Bake crackers for about 12-15 minutes, until crisp and golden around the edges. Let cool for about 10 minutes then break into crackers. Transfer to an airtight container.