In a large saucepan cook onion in hot oil until tender. Add tomatoes, broth, water, tomato sauce, sage, salt, and pepper. Bring to boiling; reduce heat. Cover; simmer for 30 minutes. Remove from heat and cool slightly.
Meanwhile, cook tortellini according to package directions; drain. Press tomato mixture through a food mill. (Or, place one-third to one-half of the mixture at a time in a blender container or food processor bowl. Cover and blend or process until smooth.)
Return mixture to pan. Add drained tortellini; heat through. To serve, ladle into soup bowls; sprinkle with cheese. If desired, garnish with sage. Makes 6 side-dish or 4 main-dish servings.