Heat olive oil in a large saucepan over medium heat until shimmering. Add broccoli and cook, stirring occasionally, until lightly browned in spots, about 5 minutes. Add garlic, oregano, and chile flakes. Cook, stirring constantly, until fragrant, about 30 seconds. Add wine and cook until slightly reduced, about 2 minutes. Add tomatoes and reserved juice. Bring to a boil, reduce to a simmer, cover, and cook, stirring occasionally, until broccoli is completely tender and broken down, about 1 hour. Season to taste with salt.
Bring a large pot of salted water to a boil and cook pasta according to package directions. Drain and add to sauce. Add parsley leaves and stir to combine. Serve immediately, garnishing with additional extra-virgin olive oil and parsley leaves as desired.
