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Bring a large pot of salted water to a boil. Add the pasta and cook according to package directions until al dente. Meanwhile, place 3 tablespoons of the oil, vinegar, and a few grinds of pepper in a small bowl and whisk to combine; set aside.
Drain the pasta and run briefly under cool water to cool it down. Drain well again. Place in a large bowl and set aside.
Heat the remaining 1 tablespoon oil in a large, deep sauté pan over medium heat until shimmering. Add the broccoli and cook until crisp-tender, 5 to 7 minutes. Transfer to the bowl with the pasta.
Crumble the feta cheese into the pasta, add the olives, and gently stir to combine. Add the dressing and toss to combine; Taste and season with salt and pepper as needed. Refrigerate until serving or overnight.