Press the pimentos between paper towels to absorb any excess moisture. Cut them into a few pieces if they're whole. (It seems the ones available in Canada are most often chopped.) If you're using block cheese, cut it into chunks.
Combine the cheeses and pimentos in a food processor and pulse a few times to begin chopping them. Add the mayo, salt and cayenne and process until the mixture has the texture of tiny-curd cottage cheese, scraping down the side of the bowl as needed. If you'd like to process it further, it will be more like a spread, and that's fine.
Scrape into a crock, bowl or jar and refrigerate for at least 4 hours before serving. Makes about 2 cups.