Heat oil in a large skillet over medium heat and soften onion, carrot and celery for 6 minutes. Add beef and pork and cook for 8 to 10 minutes, breaking them finely, until both reach 160°F; stir in garlic for 1 minute.
Add the meat-sauce milk and simmer for 3 minutes until mostly absorbed. Stir in passata, broth, 1/2 teaspoon salt and pepper and simmer for 10 minutes, leaving the sauce loose enough to spread.
Meanwhile, melt béchamel butter in a saucepan and stir in flour for 1 minute. Gradually whisk in its measured milk, remaining salt and nutmeg; simmer for 4 to 5 minutes until lightly thickened.
Butter a 6-quart slow cooker and spread 3/4 cup meat sauce over the bottom. Divide noodles into three equal groups, breaking sheets to fit without thick overlaps.
Layer one group of dry noodles, one-third of the béchamel, one-third of the remaining meat sauce and one-third of the mozzarella. Repeat twice, keeping every noodle edge covered, and finish with Parmesan.
Cover and cook on low for 3 1/2 to 4 hours, checking at 3 hours, until a knife slips through the center noodles and the filling reaches 165°F. Stop when the sheets are tender rather than leaving the lasagna for a full meat-braise day.
Switch off, uncover and rest for 25 minutes. Cut into eight portions and lift with a wide spatula; do not boil the oven-ready sheets before layering.