"Different kind of cracker. Rye flour takes longer to cook then bleached all purpose and it has a little after taste. It mixes well with Cheddar cheese. For people that have not experienced the flavor of rye, it is a nice surprise when they taste the cracker for the first time. Most of the reactions say they taste the Cheddar cheese aftertaste, not realizing it is the rye they are enjoying."
Mix Cheddar cheese, rye flour, walnuts, butter, salt, white pepper, paprika, and cayenne pepper together in a bowl until dough kneads easily. Roll dough onto a flat work surface using a rolling pin until dough is very thin. Cut dough into squares and place on baking sheet 1/2-inch apart. Puncture each cracker with a fork a few times.
Place the baking sheet in the oven and reduce heat to 400 degrees F (200 degrees C). Cook crackers until crisp, 15 to 18 minutes. Cool crackers on baking sheet, about 3 minutes.