Bring 6 quarts of water to a boil and add 2 tablespoons salt.
In a large skillet, heat the olive oil over medium-high heat and add the skate, garlic, and parsley. Cook over high heat for 5 minutes, then add the tomatoes, broccoli, and salt and pepper, to taste. Simmer for 10 minutes.
Meanwhile, cook the linguine in the boiling water according to the package directions, until tender yet al dente. Drain the pasta and add it to the pan with the skate sauce. Toss over high heat 1 minute and serve, evenly divided among 6 warm pasta bowls.