1. Bring large pot of lightly salted water to a boil.
  2. Meanwhile, in large nonstick skillet, heat oil over medium-high heat. Add onion and fennel and cook, stirring often, until softened, about 5 minutes. Add garlic and fennel seeds and cook, stirring, 1 minute. Stir in broth and lima beans and bring to a simmer.
  3. Stir in green beans and salt, reduce heat to medium and simmer until all beans are tender, 15 to 20 minutes.
  4. Add tomatoes and simmer, stirring occasionally, until flavors have blended, about 5 minutes. Stir in parsley and pepper.
  5. Shortly before sauce is ready, add bow ties to boiling water; stir to prevent sticking. Cook, stirring often, until just tender, 8 to 10 minutes. Drain well and place in large warm serving bowl.
  6. Add bean mixture and toss to coat. Serve sprinkled with Parmesan if desired.
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