Preheat oven to 250ºF. Cut a round of parchment paper to fit the diameter of a 5- to 6-quart Dutch oven or a wide heavy saucepan with a lid. Cut a small hole in center of the parchment round.
In the Dutch oven or saucepan, heat 1 ½ tablespoons of oil over medium heat until hot but not smoking. Add the onion and carrots and cook until tender and lightly golden, about 10 minutes. Add the wine and continue cooking for another 2 minutes. Add the stock, tuna and anchovies; increase the heat to high and bring the liquid just to a boil, then remove the pot from the heat. Add the veal and make sure it is mostly submerged in the liquid (add up to 1 cup water, if needed, to just cover the meat), then cover with the prepared parchment paper and the lid. Transfer pot to the oven and bake until the internal temperature of the veal reaches 135ºF, about 1 ½ to 2 hours.
Transfer the veal and the braising liquid (including the solids) to a large, nonreactive bowl; cover and al – low the meat to cool completely in the refrigerator. Once cool, remove the veal from the braising liquid (reserving the liquid and solids), and refrigerate, covered, until ready to use, up to 36 hours.
Using a slotted spoon, transfer all the solids from the braising liquid to a blender, 1 tablespoon of the capers, and enough of the braising liquid to cover the solids by ½ inch. Purée to combine. Add the yolks from the hard-boiled eggs and the mustard. Continue to purée until smooth. Stream in more of the braising liquid by the spoonful to the blender as you purée, thinning as you go until you reach the consistency of a loose custard. Season with salt to taste. Then, with the blender running, add 1 ½ tablespoons extra-virgin olive oil and 1 tablespoon fresh lemon juice, and purée until creamy and smooth.
Refrigerate, covered, until thickened and chilled, at least 1 hour and up to 2 days.