Preparation Bring a large pot of water to a boil over medium-high heat. Gently lower cold eggs into water. Cook 10 minutes, then drain and transfer to a large bowl of ice water. Carefully peel eggs and cut in half lengthwise. (To get clean cuts, use a very sharp knife and wipe the blade between each cut.) Pop out yolks and transfer to a food processor. Arrange whites on a platter. Add tuna, anchovies, mayonnaise, lemon juice, and 2 tsp. capers to food processor and purée until smooth. Add salt and 2 Tbsp. oil and pulse just until combined. Transfer to a pastry bag or resealable plastic bag and snip the corner. Pipe into egg whites. Cook remaining 4 tsp. capers and 2 Tbsp. oil in a small skillet over medium heat, stirring occasionally, until capers are crispy, 3–4 minutes. Transfer to a paper-towel-lined plate and let cool. Top eggs with crispy capers and salmon roe (if using). Do Ahead: Whites and filling can be made 1 day ahead. Tightly cover egg whites on baking sheet or platter and chill. Store filling in tightly sealed bag and chill.
Preparation Bring a large pot of water to a boil over medium-high heat. Gently lower cold eggs into water. Cook 10 minutes, then drain and transfer to a large bowl of ice water. Carefully peel eggs and cut in half lengthwise. (To get clean cuts, use a very sharp knife and wipe the blade between each cut.) Pop out yolks and transfer to a food processor. Arrange whites on a platter. Add tuna, anchovies, mayonnaise, lemon juice, and 2 tsp. capers to food processor and purée until smooth. Add salt and 2 Tbsp. oil and pulse just until combined. Transfer to a pastry bag or resealable plastic bag and snip the corner. Pipe into egg whites. Cook remaining 4 tsp. capers and 2 Tbsp. oil in a small skillet over medium heat, stirring occasionally, until capers are crispy, 3–4 minutes. Transfer to a paper-towel-lined plate and let cool. Top eggs with crispy capers and salmon roe (if using). Do Ahead: Whites and filling can be made 1 day ahead. Tightly cover egg whites on baking sheet or platter and chill. Store filling in tightly sealed bag and chill.