Add the oil to a large skillet and heat to medium-high. Add the beef and sausage and cook until browned, crumbling into small pieces, around 5 minutes. Drain excess fat.
Add the beef broth and pasta sauce and stir to combine.
Layer in the lasagna noodles by pushing them down into the sauce. Create a single layer.
In a small dish, mix together the ricotta, 1/2 cup of the mozzarella, salt, pepper, and garlic. Scoop small dollops into the skillet, about half of the mixture. Layer with more noodles, pressing them down into the sauce. Repeat adding the cheese mixture, and then a final layer of noodles. Gently agitate to ensure all the noodles are covered.
Bring mixture to a boil, then reduce heat to low, cover, and allow to simmer for 15 minutes.
Uncover, add the remaining mozzarella, and recover for another 5 minutes. Remove from heat.
Allow to sit for a couple minutes before serving, then garnish with parmesan and fresh basil.