Grate cheddar in food processor or on hand grater.
Add cheese to a large bowl with sugar, Miracle Whip or Mayo and stir to combine.
Add back to food processor with the blade attachment instead of the grating attachment.
Pulse the processor until you get your desired consistency.
Add half of the pimentos and some of the liquid from the jar. This will loosen the cheese mixture in the food processor a little and should allow it to become a bit smoother.
When the cheese mixture looks like it would be spreadable, taste it and add any salt and pepper that it might need.
Add the remaining pimentos and all the liquid from the jar and pulse one or two more times. This will allow your pimento cheese to have visible pimentos in it. If you add the pimento all at the beginning, you will blitz it until it's all too small to see.
Package up the pimento cheese and store in the fridge for a week or so.
From my Mom's notes: "We take this to the beach each year and it is best enjoyed with Bugles as a snack. Dip the Bugles in the pimento cheese and make small ice cream cone 'look-a-likes.'"
Add some diced pickled jalapenos and stir them in at the end of the process if you want to add some spice to your pimento cheese.