Cube the cream cheese. Place it in a medium microwave-safe mixing bowl. Microwave for 30 seconds.
Add the mayonnaise, Dijon mustard, minced garlic, and smoked paprika. Mix with a rubber spatula, then use a hand whisk to whisk the mixture until smooth.
Using a rubber spatula, mix in the shredded cheddar and the pimientos. Mix well, until the mixture is uniform.
Transfer the pimiento cheese to a serving bowl. Cover and refrigerate for 30 minutes, or until ready to serve. If refrigerating for longer than 30 minutes, remove from fridge 15 minutes prior to serving. Mix again before serving.
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Notes
I like my pimento cheese chunky, so I simply mix everything by hand. But some people like to use their food processor and create a smoother texture. Although the peppers should still remain chunky, so if you do use the food processor, you should add them last and process them for just a few seconds.You can keep the leftovers in the fridge, in an airtight container, for up to 4 days. I don't recommend freezing this cheese. Its texture will be off after thawing.