Heat 6 tablespoons olive oil in a large skillet over medium heat, then stir in garlic, broccoli, and mushrooms; cook until lightly browned. Add anchovies and water, cover, and simmer for 4 to 5 minutes. Stir in green onions, tomatoes, and parsley, cover again, simmering until vegetables are soft, about 3 to 4 minutes.
While the vegetables are cooking, bring a large pot of water and one teaspoon of olive oil to a boil. Add linguine and cook until al dente, about 7 to 8 minutes; drain. Toss with anchovy mixture and crushed red pepper flakes. If desired, season with black pepper. Serve immediately.