Let grated cheddar and Gouda stand at room temperature for 10 minutes while draining and blotting the pimentos. Chop any large pimento pieces smaller.
Stir mayonnaise, Dijon, cayenne and black pepper together in a bowl. Fold in both cheeses and the pimentos until evenly coated, without processing the mixture smooth.
Divide the spread among eight bread slices and smooth it into an even layer to the corners. Close with the remaining bread and press only lightly.
Cover and refrigerate for 15 minutes to firm the filling. Trim crusts with a sharp serrated knife, wiping the blade whenever cheese builds up on it.
Cut each sandwich into three equal fingers for 24 pieces. Serve two per portion and keep covered and refrigerated until serving, using within 24 hours.