1. Bring a large pot of water to a boil; add salt. Stir in pasta and cook until al dente, about 9 minutes. Reserve 1 cup cooking liquid, then drain pasta.
2. Meanwhile, heat 3 tablespoons oil and the butter in a large deep skillet over moderate heat until butter is melted. Add onion and oregano, season with salt and pepper, and cook until softened, about 5 minutes. Add zucchini and squash; cook, stirring frequently, until wilted, about 5 minutes. Add broth; bring to a simmer. Remove from heat and keep warm, covered, for sauce.
3. Add pasta and 1/2 cup reserved cooking liquid to sauce in skillet; toss to combine. Season with salt and pepper. Simmer until pasta is coated well, about 2 minutes. Remove from heat and toss in feta. Spoon into bowls, drizzle with remaining 2 tablespoons oil and serve. Makes 4 to 6 servings.