Preheat the oven to 375 degrees . In a medium skillet, heat 2 tablespoons olive oil over medium-high heat; add the onion and cook for 3 minutes. Add the mushrooms and cook until softened, about 5 minutes; season with salt and pepper.
Fill the tomatoes with the mushroom mixture; transfer to an 8-inch square baking dish. Pack down the filling, crack 1 egg on top of each and season with salt and pepper. Bake until the egg whites are just opaque, 20 to 25 minutes. Sprinkle with the parsley.
Meanwhile, preheat an oiled grill pan to medium-high. Season the steak with salt and pepper and grill, turning halfway through, for 12 to 14 minutes for medium-rare. Transfer to a cutting board and let rest for 10 minutes before thinly slicing.
In a salad bowl, whisk together the lemon juice and remaining 1 tablespoon olive oil; season with salt and pepper. Add the watercress and toss. Serve with the steak and tomato-baked eggs.