Preheat oven to 375ºF. Grease a 9×13-inch casserole dish.
Heat oil in a large, heavy saucepan over medium-high heat. Brown the ground meat thoroughly, breaking it up into small pieces, about 8-10 minutes.
Drain excess fat from meat using a colander.
Return the pan to heat, and add onions to the drained meat. Cook until onions are soft and translucent, about 5 minutes. Add garlic, and cook 1 minute more.
Add dried herbs and crushed tomatoes. Bring to a boil, then reduce heat and simmer for 15-20 minutes, stirring occasionally. Season with salt and pepper to taste.
Meanwhile, cook tortellini according to package directions but undercook by 1 minute. Drain well.
Spread 1 cup meat sauce in the bottom of greased casserole dish. Layer half the tortellini, top with 3/4 cup cheese, add dried basil, and spread half the remaining sauce. Repeat layers. Top with remaining cheese.
Cover with foil and bake 15 minutes. Remove foil and bake 5-10 minutes more until cheese is melted and bubbly.