Preheat the oven to 500 degrees F. Bring a large pot of salted water to a boil over high heat.
Spread out the broccoli florets on a rimmed baking sheet and toss them with 1/4 cup of the olive oil and the salt. Transfer to the preheated oven and roast for 10 minutes, stirring halfway through.
Meanwhile, add the orecchiette to the boiling water and cook until al dente, 9 to 10 minutes. Drain well, reserving 1 cup of the pasta water for the sauce.
While the pasta cooks, heat a large skillet over medium heat. Add the remaining 1/4 cup olive oil, the anchovy paste and the garlic to the hot pan. Cook, mashing up the anchovy paste with a wooden spoon, until the anchovy has dissolved into the oil and the garlic has become softened and aromatic, about 3 minutes. Add the pasta, the roasted broccoli, and the parsley, red pepper flakes, pecorino, lemon zest, raisins and pine nuts to the skillet. Stir well to combine. Add pasta water as needed to loosen the sauce.