Beef with Broccoli Pad Thai

Name: Beef with Broccoli Pad Thai
Ingredients: 1/2 pound pad Thai rice noodles (banh pho); 2 tablespoons Asian fish sauce; 2 tablespoons oyster sauce; 2 tablespoons sugar; 1 tablespoon soy sauce; 1 tablespoon tamarind paste (see Note); 1 tablespoon Sriracha or chile-garlic sauce; 2 tablespoons vegetable oil; 1/2 pound skirt steak, thinly sliced crosswise; 1/2 pound broccoli, stem trimmed and cut into 1-inch pieces; 2 small shallots, thinly sliced; 2 garlic cloves, thinly sliced; 2 cups julienned carrots (from about 3/4 pound carrots); 4 scallions, cut into 1-inch pieces; 2 large eggs, lightly beaten; 1 cup bean sprouts; 1/4 cup ground roasted peanuts; 1 lime, cut into 8 wedges, for serving