Beat the beef roulades as thinly as possible. Season with salt, pepper, and a pinch of cayenne pepper.
Soak the roll in roughly 60 ml of the milk, then squeeze it out very firmly.
In a food processor, combine the veal sausage, ham pieces, salami, 2 cloves of garlic, toasted pine nuts, anchovy fillets, dried tomatoes, and parsley. Pulse until combined. Mix in the parmesan and soft butter or olive oil. Add the squeezed roll and egg, then mix until well combined. Season to taste with salt and pepper. Set aside about 1 tablespoon of this mixture for the sauce.
Divide the remaining filling evenly among the roulades and spread it out smoothly. Roll up each roulade and secure with kitchen twine or roulade clamps so the filling doesn't escape.
In a large roasting pan, heat 1 tablespoon of olive oil over medium heat. Add the reserved filling, 3 whole garlic cloves, and half of the diced onion. Fry for 3–4 minutes until the garlic begins to soften and turn light brown. Flatten the garlic slightly with a fork and continue frying for 1–2 minutes until light golden (do not let it burn). Remove from the pan and set aside.
In the same pan, brown the roulades over medium heat on all sides, about 10–12 minutes total. Add the remaining onion and carrot, then fry for 2 minutes. Pour in the Marsala and use a spatula to scrape the bottom of the pan to release the browned bits. Reduce heat to low and simmer for 5–10 minutes until the wine has mostly evaporated.
Dust the roulades with 2 tablespoons of flour and gently move them around for 2–3 minutes until the flour is light golden brown. Add the tomatoes (crushing them slightly if whole) and pour in enough water or broth to just cover the roulades. Add the fresh basil, ½ teaspoon dried oregano, ½ teaspoon dried thyme, ½ teaspoon dried sage, and the bay leaves. Bring to a boil over high heat, then reduce to low heat for a gentle simmer.
Simmer for 2 to 2.5 hours, until the meat is very tender and a fork pierces it easily. Check occasionally and adjust seasoning with salt and pepper as needed.
Remove the roulades very carefully with tongs and keep them warm on a separate plate.
Optional: Use an immersion blender to puree the sauce, or leave it as is with the vegetable pieces. Increase heat to medium-high and cook the sauce for 5–10 minutes until it reaches your desired thickness. Season again with salt and pepper.
Remove the kitchen twine or clamps from the roulades. Cut each roulade diagonally into slices and arrange on serving plates or over cooked pasta. Pour the sauce around or over the meat. Serve immediately. The braciole can be frozen well, covered with sauce.
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