In a large pot, bring 2 quarts water to a boil. Gradually stir in pasta and return to a boil. Cook uncovered for about 8-10 minutes until tender. Do not overcook. Drain well.
Heat olive oil in a large skillet over medium heat. Add half of tomatoes and cook 2-3 minutes until skins soften. Do not overcook. Reserve remaining tomatoes for step 4. Add basil, salt, pepper, and garlic. Stir.
Sprinkle flour over tomatoes. Cook for 30 seconds over medium heat until mixture becomes thick. Add vegetable broth. Bring to a boil and then immediately reduce to low heat.
Add Swiss chard and remaining tomatoes. Simmer uncovered over low heat for 1-2 minutes or until Swiss chard is wilted. Pour over pasta. Serve hot.