Chop and brown the onion, garlic and bits of the swordfish trimmings in 1 tbs. oil. Add the parsley, basil, breadcrumbs and capers. Cook for 2 min., and then remove from heat, cool, and pass through a food mill. Combine the diced cheese and the eggs with the mixture. Add salt and pepper to taste and work into smooth filling.
Flatten the swordfish fillets slightly with a mallet and place a spoonful of filling in the middle. Roll up the fillets and close with toothpicks. Cook the swordfish rolls either broiled or or sauté ed in olive oil.