Heat a medium Dutch oven over medium heat. Toss in 1 tablespoon of butter and 2 tablespoon of olive oil. Heat them until the butter melts.
Throw in the chopped onion, carrots, celery, and ½ teaspoon salt. Cook for 6 minutes, stirring often. You want them soft but not browned.
Add the ground chuck. Break it apart with a wooden spoon. Cook for 5 minutes or until it's no longer pink.
Mix in the chopped garlic, chili paste, and tomato paste. Cook for 2 minutes, stirring a lot to caramelize the tomato paste and cook the garlic gently.
Sprinkle in another ½ teaspoon salt and pour in the milk. Let it simmer for 20 minutes, stirring now and then until the milk is mostly gone.
Pour in the red wine, add the crushed tomatoes, bay leaf, and Parmesan rind. Lower the heat and keep it at a gentle simmer for 1 ½ hours, stirring occasionally. Skim off any oil that forms on the surface. Season with the last ¼ teaspoon of salt.
Let the sauce cool to room temperature, stirring often, for about an hour. Fish out and toss the Parmesan rind and bay leaf. The sauce should be cool or just warm.
Boil a large pot of salted water. Cook the pasta until it's quite al dente, about 3-4 minutes less than the package says. Scoop the pasta out to a baking sheet to cool. Save ¼ cup of the pasta water and let it cool too.
Spread ½ cup of sauce in a 9x13 inch baking dish. Mix the cooled pasta with 1 cup of grated Parmesan and the cooled sauce. Toss well. Layer it in the baking dish. Top with the remaining ½ cup of Parmesan and all the mozzarella. Cover with plastic wrap and chill until you’re ready to bake.
Heat your oven to 375°F. Take the dish out of the fridge 30 minutes before baking. Drizzle the reserved pasta water over the pasta. Cover tightly with foil. Bake for 30 minutes. Then crank the heat to 425°F, remove the foil, and bake until golden and bubbly, about 25 more minutes.
Let it rest for 5 minutes after baking. Then it’s ready to hit the table and wow everyone.