Grate the cheddar in food processor or on hand grater.
Add cheese to a large bowl with sugar and mayonnaise and stir to combine.
Add the cheese mixture back to the 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 cayenne pepper powder. You can adjust how spicy you want the pimento cheese at this point. Use the larger amount for an extra spicy kick.
Add the jalapenos, the remaining pimentos and all the liquid from the pimento jar and pulse one or two more times. This will allow your pimento cheese to have visible jalapenos and pimentos in it. If you add the jalapenos and pimentos 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.