I directly associate this snack with tomato soup, the perfect pairing throughout junior high, when consumed post-soccer practice in front of reruns of "The Rockford Files."
The dough for our recipe is prepared in a food processor because, as gail the baker explains, "the sharp blade and its fast rotation cuts the cheese into tiny bits quickly, dispersing them through the dough to promote a flakier texture." If you spooned these out into little balls, people would think they were a high-end cocktail snack. Cut into squares, with a neatness level that will depend on how compulsive you are, they are a bagged lunch treat completely loyal to the original. The paprika is responsible for the tang; the better the cheese you use, the sharper and more elegant the taste, yet they will still remain distinctly Cheez-It-esque.
In a food processor, pulse the flour, baking powder, salt, and paprika together 3 to 5 times, until just combined. Add the cheddar cheese and pulse 15 to 20 times, or until the cheese is finely chopped. With the motor running, slowly pour in the vegetable oil and continue to process just until all the oil is incorporated. Wrap the dough in plastic, shaping it into a disk. Freeze for 2 hours, or until the dough just gives when pressed but holds its shape when picked up.
Preheat the oven to 450°F. Line two baking sheets with parchment paper.
Unwrap the dough and divide in two equal pieces. Place half of the dough on a piece of parchment paper and shape into a rectangle with your hands. Lightly sprinkle the top of the dough with flour and roll out, keeping the rectangle shape, to a thickness of just under 1/4 inch. Using a pizza cutter or metal bench scraper, cut the dough into 1-inch squares. Transfer the squares on the parchment to the prepared baking sheet and carefully separate them, spacing them evenly, about 1 inch apart. Repeat with the second batch of dough.
Bake the squares for 7 to 9 minutes, or until the crackers are golden and the edges are beginning to brown. Cool completely on wire racks. Store in an airtight container for up to 3 days.