In the bowl of a food processor, process the cheese and butter for 30 seconds or just until combined.
With the machine running, slowly pour the oil through the food chute. Then add the flour, mustard, and red pepper, and process another 30 seconds or just until the mixture resembles coarse crumbs. (To keep the wafers flaky and tender, avoid over-processing.).
Remove the dough, press into a ball, and roll in plastic wrap. Place on flat plate and let chill in refrigerator for 30 minutes.
Preheat oven to 350°F, and set out two ungreased baking sheets.
Shape the dough into 40 balls, about 1/2-inch in diameter, and place them 2 inches apart on the baking sheets. Using the back of a fork, lightly flatten each ball twice, making a criss-cross pattern, until the dough resembles a coin about 1/8-inch thick.
Bake at 350°F for 15 minutes or just until crisp but not browned. Transfer to wire rack, dust the tops lightly with paprika, and let cool.
Store in air-tight container for up to 2 weeks, or you can freeze it for up to 3 months.