Grate the 8oz sharp cheddar cheese and 8oz extra sharp white cheddar cheese. Mix the grated cheese well with a rubber spatula in a large bowl.
Add the 4oz softened cream cheese to the grated cheddar cheese. Mix until the cream cheese is evenly incorporated, breaking up any large clumps.
Add the 1/2 cup mayonnaise, 1/4 cup sour cream, 2 tablespoons adobo sauce, 2 tablespoons minced pimentos, 1 teaspoon Worcestershire sauce, 1/2 teaspoon garlic powder, 1/2 teaspoon onion powder, 1/4 teaspoon kosher salt, and 1/8 teaspoon freshly ground black pepper. Mix thoroughly until uniform.
Use the rubber spatula to scrape down the sides of the bowl, ensuring all ingredients are fully mixed together. Mix vigorously for 1-2 minutes until completely smooth.
Transfer pimento cheese to an airtight container, smooth the top evenly, cover, and refrigerate for at least 2 hours before serving.
Scoop desired portions to serve, packing firmly back down. Cover and store leftovers in the fridge for up to 1 week.