Preheat oven to 350° F. Line 12 jumbo muffin tins with squares of parchment paper that cover the entire inside of each tin. If they don't stay in on their own, that's ok - the pasta will help with that.
Line the edges of the muffin tins with 1 pasta sheet per cup. Pasta sheet will overlap about 2 inches.
Spoon about half a tablespoon of sauce into the bottom of each cup.
Next, cut 9 pasta sheets into quarters and press one of these pieces of pasta into the bottom of each tin, on top of the sauce.
Top pasta sheet with a generous tablespoon of sauce and then a generous tablespoon of cheese filling.
Repeat this pasta-sauce-cheese layering one more time, pressing down to remove any air bubbles.
Top these lasagna cups off with the third piece of pasta, more sauce and the remaining mozzarella cheese.
Cover with a gentle aluminum foil tent (to prevent edges from getting too crispy). Bake for 25-30 minutes or until everything is hot and bubbly. Serve hot.