Season steak with paprika, salt, and pepper all over. Add soy sauce, Worcestershire sauce, mustard, and hot sauce to a resealable bag. Add steak and toss around to make sure steak is covered. Refrigerate for 2 hours.
Remove steak from marinade and discard extra marinade. In a large skillet over medium heat, heat oil. Add steak and cook tossing around for 5 minutes. Remove from skillet.
Return skillet over medium heat and melt butter. Add garlic and cook until fragrant, 1 minute. Add mushrooms and thyme and cook until mushrooms are golden, about 5 minutes. Return steak to skillet and toss to warm through.