Cook the lasagna noodles according to the package. Be sure to save some pasta water, drain, then spread the noodles out to prevent clumping.
Melt 4 tablespoons of butter over medium heat, add the onions. Caramelize for as long as your patience will allow (low and slow is best). Once a few minutes from being done, add the garlic and balsamic vinegar. Cook for a few final minutes until it is all golden brown and lightly crispy.
Add the heavy cream and bring to a simmer then add the pasta water and stir frequently for a few more minutes over medium-low heat. Add the parmesan cheese and stir until dissolved.
Begin assembling your rolls by extending the noodles, spreading a couple tablespoons of sauce onto each. Add shredded chicken and mozzarella cheese as your heart desires. Roll tightly.
Grease a casserole dish, add the rolls, and cover with the remaining alfredo sauce. Top with a layer of mozzarella cheese.
Bake in the oven for 10 minutes at 400F or until golden and bubbling. Allow to cool and enjoy!
