In a large sauté pan, heat 2 tablespoons olive oil over medium heat. Add mushrooms, shallots, parsley, and garlic. Cook until vegetables are tender, 4 to 5 minutes, stirring frequently.
Add sherry, cream, ½ teaspoon salt, and ¼ teaspoon pepper. Simmer until liquid is completely absorbed, 15 to 20 minutes, stirring frequently. Remove from heat and cool slightly.
Preheat oven to 400°.
Line a baking sheet with parchment paper. Set aside.
Sprinkle remaining ½ teaspoon salt and ¼ teaspoon pepper evenly on beef fillets. Set aside.
In a medium skillet, heat remaining 2 tablespoons olive oil over medium-high heat. Cook fillets in hot oil until browned, 2 to 3 minutes per side. Transfer fillets to prepared pan.
Bake until internal temperature of meat registers at least 145° (rare) on an instant-read thermometer, 10 to 15 minutes. Remove from oven, and let steaks rest for 2 minutes.
Thinly slice steaks into 24 pieces.
To assemble, spread 1 teaspoon Chive and Horseradish Cream on each Crostini. Spoon 2 teaspoons mushroom mixture on top of cream. Place a slice of beef on top of mushroom mixture.
Garnish with additional Chive and Horseradish Cream and fresh chives, if desired.