Preheat the oven to 450 degrees F. Toss the sausage, broccoli, 1 tablespoon vegetable oil and a pinch each of salt and pepper on a baking sheet. Bake, stirring, until the sausage is browned and the broccoli is charred, 25 to 30 minutes.
Meanwhile, whisk the flour, baking powder, 1/4 teaspoon salt and 1/2 teaspoon pepper in a large bowl; make a well in the center. Separate 2 eggs, putting the whites in a large bowl and the yolks in the well in the flour. Whisk the milk, 2 tablespoons vegetable oil and 1/2 tablespoon teriyaki sauce into the yolks, then whisk into the flour; stir in the scallions. Whisk the egg whites until stiff; fold into the batter.
Heat a large nonstick skillet over medium-high heat; brush with vegetable oil. Ladle ¼ cup batter into the skillet for each pancake. Cook, flipping once, until golden, about 4 minutes. Keep the pancakes warm on a baking sheet in the oven as they are done.
Heat the remaining 1 tablespoon vegetable oil in the skillet and crack in the remaining 4 eggs; season with salt and pepper. Cook until the whites are set but the yolks are still runny, 3 minutes. Whisk the remaining 2 1/2 tablespoons teriyaki sauce, the sesame oil, vinegar and 1 teaspoon water in a small bowl.
Divide the pancakes, broccoli, sausage and fried eggs among plates. Serve with the sauce.