Heat olive oil in a large skillet. Saute onion and carrot 5 minutes or until tender, stirring occasionally. Set aside and allow to cool.
Combine beef, 1/2 cup tomato sauce, panko, egg and parmesan in a large bowl, gently mix until combined. Add cooled vegetables and fresh basil and mix until combined.
Fill 10 muffin cups to the top with meat mixture. Spoon remaining tomato sauce evenly over each muffin.
Bake at 350° for 25 minutes or until a thermometer registers 160°. Let stand for 5 minutes.