Pat the beef tips dry with paper towels, and season with salt and pepper. Set the cast-iron skillet over medium-high heat, and when the skillet is hot, add the safflower oil. Add the beef, and saute just until brown on all sides -- about 2 minutes. Transfer the beef to a plate and keep warm.
In the same skillet, melt the butter. Then add the sliced mushrooms, and saute them until soft and colored -- 1-4 minutes depending on the thickness of the slices. Add the wine or vermouth, and as it boils, use a spatula to scrape up all the flavorful bits of meat that have stuck to the pan. Then stir in the scallions, Worcestershire Sauce, mustard, salt and pepper (to taste), and the tarragon leaves.
Turn off the heat, and then immediately return the beef to the skillet. Stir the beef into the mushroom mixture. Garnish with thin slices of scallion, and serve.