In the bowl of a food processor, process the cheese and butter for about 30 seconds, or just until combined. With the motor running, slowly pour the oil through the feed tube.
Then add the flour, mustard, and red pepper. Process for 30 seconds, or just until the mixture resembles coarse crumbs. (To keep the wafers flaky and tender, avoid overprocessing.) Remove the dough from the food processor, press into a ball, roll in plastic wrap, and refrigerate 30 minutes.
Preheat oven to 350°F and set out 2 ungreased baking sheets. Shape the dough into 40 balls, 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 15 minutes, or just until crisp but not browned. Transfer to wire racks, dust lightly with paprika, and let cool. Store in an airtight container up to 2 weeks or in the freezer up to 3 months at 0°F.