Adjust oven rack to upper-middle position, place rimmed baking sheet on rack, and heat oven to 400 degrees. Using sharp knife, cut ¼-inch slits, spaced ½ inch apart, in crosshatch pattern on surface (non-gill side) of mushrooms.
Brush both sides of mushroom caps with 2 tablespoons oil and sprinkle with salt. Carefully place caps gill side up on preheated sheet and roast until mushrooms have released some of their juices and begun to brown around edges, 8 to 12 minutes. Flip caps over and continue to roast until liquid has completely evaporated and caps are golden brown, 8 to 12 minutes. Transfer mushrooms to plate and let cool slightly.
Spread cream cheese over gill side of mushroom caps and arrange on 2 individual serving plates. Top with salmon, eggs, capers, shallots, and parsley. Sprinkle with pepper to taste and drizzle with lemon juice and remaining 1 tablespoon oil. Serve.