Arrange bread in a large baking dish. Pour milk over bread; allow to soak until bread is soggy. Remove bread and squeeze excess moisture from the bread. Discard milk.

Whisk anchovy paste with eggs in a bowl until dissolved.

Crumble tuna and moistened bread together in a large bowl. Add the egg mixture, parsley, capers, and Parmesan cheese; knead together until evenly blended and reasonably firm. Wrap the mixture in a clean cotton dishtowel and roll it up tightly, securing the two ends with string or elastic bands.

Bring a large pot of lightly salted water to a boil. Cook the bundled tuna loaf in boiling water for 40 minutes; drain. Chill in refrigerator until cold before unwrapping and slicing to serve.