Reserve 1-1/4 cups stock. Bring remaining stock to a boil in a large pot, add tortellini and cook until tender, drain well.
In a small bowl, blend cornflour into 1 1/4 cups of reserved stock.
In a large saucepan, saute garlic and basil in the butter or margarine for 2 minutes over a medium heat. Add the cornflour-stock mixture to the saucepan. Cook and stir until the mixture thickens and comes to a boil.
Place tortellini in a serving dish, pour the stock-mixture and Parmesan cheese into the serving dish and toss. Serve with toothpicks.