Gather your ingredients so that you have everything close at hand.
Prepare the Ingredients
Using a box grater, shred the sharp cheddar cheese. You could also opt to use extra sharp cheddar for this recipe.
Place the cheddar cheese crackers in a food processor and pulse until the crackers are completely crushed. The more powdery they are, the better they will stick to the cheese. Place crushed crackers in a bowl for dipping.
Make the Cheese Balls
Place the shredded cheddar cheese, chopped pimentos, 1/2 cup of the crushed crackers, dried minced onion, minced garlic, smoked paprika, kosher salt, and freshly ground black pepper in the food processor. Pulse until smooth.
Transfer the cheese to a bowl and cover with a lid or plastic wrap. Refrigerate for 30 minutes.
Using a tablespoon or a small cookie scoop (size 60 or less), scoop up dough and roll into small balls.
Roll each ball into the remaining crushed cheese crackers to cover.
Place balls in a covered container and refrigerate at least 60 minutes before serving. When ready to serve, place toothpick in center of each ball with a stuffed green olive.