Position knife blade in food processor bowl; add Cheddar cheese and pimiento. Process 3 to 5 seconds. Stop processor, and scrape sides of bowl with a rubber spatula.
Add next five ingredients; process until smooth. Add additional mayonnaise, if necessary. Chill. Wash celery, and cut into 3-inch pieces. Using a pastry bag, pipe cheese mixture into celery pieces; sprinkle with paprika.
Note: If food processor is not available, combine ingredients in a bowl; beat with electric mixer until smooth.