Place the cheeses, pimentos, mayonnaise and mustard into the bowl of a food processor. Process until smooth and blended, about 30 to 40 seconds, stopping to scrape the sides of the bowl as needed.
Transfer the cheese mixture to an airtight container and refrigerator for at least 1 hour.
Spread the cheese mixture on bread slices and serve. The cheese mixture can keep in the refrigerator for up to 1 week.