Get all the prep done before you start cooking: mince the garlic, finely chop the shallots and dice the carrots. Remove casing from sausages, roll into meatballs.
If you like a crispy golden-brown lasagna top, turn on your broiler and use an ovenproof skillet.
Heat oil and butter in a a large high-sided skillet or a Dutch oven over medium-high. Add meatballs, brown on all sides, about 6 minutes, remove from skillet. Leaving as much grease as possible in the skillet.
Add shallot and garlic, cook for 2 minutes. Stir in salt, black pepper, paprika and sage. Add carrots, cook for 1 minute. Deglaze with white wine, simmer for 2 minutes, stir with a wooden spoon while scraping up the brown bits on the bottom of the skillet. Add chicken broth, bring to a boil. Add crushed tomatoes and slowly stir in cream cheese until melted. Bring to a simmer.
Add lasagna noodles to the skillet. Spread into an even layer and push down to submerge. Reduce the heat to medium low and simmer, uncovered, stirring occasionally to prevent noodles from sticking, about 15 minutes or until the sauce has thickened slightly.
Add meatballs together with the released juices. Top with cheddar, mozzarella and Parmesan. Sprinkle with black pepper and red pepper flakes. Cover and simmer over low, about 10 minutes. Remove from heat, sprinkle with parsley if using, let stand for 10 minutes.
Alternatively, place under the broiler for a crispy golden-brown top.