In a microwave safe bowl, place the mozzarella and cream cheese. Microwave for one and a half minutes. Remove and stir. Microwave again for 30 seconds.
Place mozarella and cream cheese mixture in a food processor with the eggs and blend until smooth.
Add remaining ingredients and process until a dough forms. It may be helpful to hold the food processor down a little bit as the dough is very sticky and our food processor moved slightly.
Preheat oven to 400 F and place baking rack in the middle of the oven. Line a baking sheet with parchment paper.
Divide the dough into six equal portions. Roll and then flatten slightly and place on the parchment paper- it should not be too thin or the rolls will cook too quickly. Ours were about 5 inches around. It helps to put a tiny amount of water (or oil) on your hands between every 2 or 3 rolls.
Place another metal baking sheet on the bottom rack of the oven. Place 6 ice cubes on this sheet and then put the rolls on the middle rack.
Bake for 12-14 minutes or until the tops are slightly browned. Remove from oven and let cool on the baking sheet. We made these buns first and then let them cool until our fish was ready for these delightful fish sandwiches.