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Fill a large pot with water and add a generous pinch of salt; bring to a rolling boil.
Add fusilli pasta and cook according to package directions until al dente (about 10–12 minutes).
Before draining, scoop out 1 cup of pasta water; then drain the pasta and set aside.
Heat olive oil in a large skillet over medium heat.
Add chopped onion and cook until softened and translucent, about 5–7 minutes.
Stir in minced garlic and red pepper flakes; cook for 1 minute until fragrant.
Pour in crushed tomatoes and vegetable broth; stir to combine.
Add dried oregano, then season generously with salt and black pepper.
Bring the sauce to a gentle simmer, reduce heat to low, cover, and cook for 15 minutes. If sauce is too thick, stir in reserved pasta water a splash at a time.
Remove skillet from heat and stir in chopped fresh basil.
Add cooked fusilli to the sauce and toss until evenly coated; if needed, add more reserved pasta water to reach desired consistency.
Divide among bowls and top with grated Parmesan cheese before serving.
Serve immediately with salad or crusty bread if desired.