Prepare steaks: Remove from refrigerator 30 minutes before cooking. If thick, pound gently to even 1-inch thickness. Pat completely dry with paper towels.
Season: Season both sides liberally with salt and black pepper. Press seasonings into meat.
Heat pan: Heat large heavy skillet over medium-high heat 3-4 minutes until very hot and almost smoking.
Sear steaks: Add 1 tablespoon vegetable oil and swirl. Place steaks in pan. Don't move—sear undisturbed 3-4 minutes until deep golden crust forms.
Flip and finish: Flip steaks with tongs. Add 1 tablespoon butter. Sear 3-4 minutes for medium-rare (130-135°F internal temp). Baste with butter.
Rest meat: Transfer steaks to plate and tent with foil. Rest 5-10 minutes while making sauce.
Start sauce: Return skillet to medium heat (don't clean—those bits are flavor). Add 2 tablespoons butter and melt. Add shallots and cook 1-2 minutes until softened.
Cook mushrooms: Add sliced mushrooms. Cook 4-5 minutes, stirring occasionally, until liquid releases and mushrooms brown. Season with salt and pepper.
Add garlic: Add garlic and cook 30 seconds to 1 minute, stirring constantly.
Flambé (optional): Remove pan from heat. Pour in cognac. If comfortable, carefully ignite with long match, tilting pan. Let flames burn out (30 seconds). Or simply add cognac and simmer 2 minutes.
Build sauce: Add beef broth and simmer 3-4 minutes, scraping up browned bits from bottom of pan.
Add cream: Reduce heat to medium-low. Whisk in heavy cream, Dijon mustard, and Worcestershire sauce. Simmer gently 3-5 minutes until sauce thickens to coat back of spoon.
Finish sauce: Add lemon juice and taste. Adjust salt and pepper. Stir in parsley and chives.
Combine: Return rested steaks and any juices to pan. Spoon sauce over steaks and warm through 1-2 minutes, turning once.
Serve: Transfer steaks to warm plates. Spoon mushroom sauce generously over each steak. Garnish with fresh herbs. Serve immediately.