Cook beef in large skillet over medium heat 6-8 minutes, stirring occasionally, until beef is no longer pink; drain and return to pan.
Add garlic and cook for 1-2 minutes.
Stir in crushed tomatoes, tomato sauce, Italian seasoning, basil, and salt. Taste, and add more salt as needed.
In a medium bowl, stir together ricotta, Italian cheese, and egg.
Spoon one-third of the beef mixture into 9x13-inch pan.
Lay cooked noodles out flat on nonstick surface like parchment paper.
Spread each noodle with about 1/3 cup of cheese mixture.
Roll noodles up, and place seam side down in pan.
Cover noodle rolls with remaining beef sauce.
Cover pan with foil sprayed with nonstick cooking spray.
Bake for 30 minutes.
Sprinkle top of lasagna rolls with remaining mozzarella cheese.
Return to oven for 3-5 minutes, or until cheese is melted.
To make-ahead, I make the rolls through step 11, and then I cover and chill them for a few hours until ready to bake. I pull the pan out of the fridge while the oven preheats and then bake as directed, adding additional baking time as needed.
To freeze the lasagna roll-ups, prepare through step 10. Cover with plastic wrap and then (ungreased) foil. Move to fridge to thaw about 24 hours before you'd like to bake the roll-ups. Remove plastic wrap. Grease foil and re-cover the roll-ups with greased foil. Bake thawed roll-ups as directed, adding additional baking time as needed.