Heat olive oil in a deep skillet over medium-high heat. Add onion, celery, and carrot; cook until softened. Add garlic and cook 1 minute. Add veal, pork, and beef. Cook, stirring occasionally, until meat is no longer pink.

Add wine and reduce for 1 minute. Stir in broth. Add rosemary, Italian seasoning, bay leaf, salt, and pepper. Bring mixture to a boil. Reduce heat, cover, and simmer for 15 minutes. Uncover and reduce until almost dry. Discard bay leaf and set aside to cool.

Melt butter in a saucepan over moderately low heat. Whisk in flour for about 2 minutes. Whisk in milk, grated nutmeg, salt, and pepper. Simmer, stirring occasionally, until thickened, about 5 minutes. Stir in 1/2 cup Parmesan cheese and parsley. Set aside.

Transfer cooled meat mixture to a large bowl and mix in egg yolks. Stir in cheese and parsley sauce; set aside.

Combine tomato sauce and cream in a bowl; set aside.

Preheat the oven to 400 degrees F (205 degrees C). Generously coat a gratin dish with butter.

Bring a pot of salted water to a boil over high heat. Cut pasta sheets crosswise into 5-inch lengths, then cook noodles, a few at a time, until al dente, 1 to 2 minutes for fresh pasta. Transfer pasta to a bowl of cold water. Spread noodles in a single layer on paper towels to drain.

Spoon 1/4 cup filling down the center of one noodle; roll noodle to enclose filling. Transfer cannelloni, seam-side down, to the prepared gratin dish. Repeat with remaining noodles and filling, arranging in a single layer.

Ladle tomato cream sauce over filled cannelloni and sprinkle with remaining Parmesan cheese.

Bake in the preheated oven until bubbling, about 10 minutes. Turn the broiler on and continue cooking until top is golden, about 2 minutes.