1/2 cup unbleached all-purpose flour, plus extra for dusting
5 tablespoons unsalted butter
1/3 cup grated Cheddar
1/4 cup grated Parmesan
20 olives stuffed with pimientos
In a mixing bowl, combine the flour and butter until the mixture resembles bread crumbs. Mix in the Cheddar and Parmesan and knead lightly to combine. Form the mixture into a disk. Wrap it in plastic wrap and refrigerate for at least 30 minutes.
Unwrap the dough, take a small piece and cover an olive, making sure the pastry surrounds the olive and there are no gaps. Flour your hands and roll the olive-encased pastry into a ball; put it on an ungreased baking sheet. Repeat the process with the remaining pastry and olives. Chill in the refrigerator for at least 1 hour. (Can be made a day ahead and held in the refrigerator.)
Preheat the oven to 425 degrees F. Put the baking sheets on the middle shelf of the oven and bake until the pastries are light golden, about 10 minutes. Remove the bites from the oven and arrange on a serving platter.