In a mixing bowl, combine the ricotta cheese, beaten eggs, and basil. Mix until fully incorporated.
In a separate bowl, combine the tomato paste with the Italian pasta sauce. Stir until smooth and evenly blended.
Lightly grease the inside of the slow cooker.
Spread 2 1/3 c sauce evenly over the bottom of the slow cooker.
Add approximately 1/3 of the uncooked penne pasta over the sauce.
Spoon a portion of the ricotta mixture over the pasta and spread it as evenly as possible.
Sprinkle 1 c freshly shredded Parmesan cheese over the ricotta layer.
Add the cooked ground beef in an even layer.
Spoon additional sauce over the ground beef.
Add another 2 1/3 c sauce over the layer.
Place another layer of uncooked penne pasta over the sauce.
Spoon another layer of the ricotta mixture over the pasta and spread evenly.
Sprinkle the remaining Parmesan cheese over the ricotta layer.
Add the remaining uncooked pasta on top of the Parmesan layer.
Pour the remaining sauce evenly over the top, ensuring the pasta is well covered.
Cover the slow cooker and cook on high for 2 to 3 hours, or until the penne is tender but still al dente.
During the final few minutes of cooking, sprinkle the freshly shredded mozzarella cheese over the top.
Cover again and allow the mozzarella to melt completely.
Serve warm with garlic breadsticks, if desired.