Pat steak dry with paper towels and season with salt and pepper. Heat 1 tablespoon oil in large stainless steel, cast iron, or aluminum skillet over medium-high heat until very hot but not smoking. Add steak tips in a single layer and sear on all sides until the exterior is nicely caramelized, 6 to 8 minutes. Depending on the size of your skillet, you might need to do this in 2 separate batches. Transfer the steak to a serving dish in a single layer, and loosely cover with foil.
Adjust the heat to low, then add the shallots to the pan along with a pinch of salt (if the bottom of the pan isn't shiny, add a small splash of oil first). Stir, using a spatula to scrape up the brown bits from the bottom of the pan. If the brown bits won’t detach or look like they might burn, deglaze the pan with 1 tablespoon of water to help loosen them.
After 1-2 minutes, add the mushrooms and garlic, turning the heat up to medium-low, and cook until the mushrooms are soft, 3-4 minutes.
Stir in the stock, cream, and any juices that have accumulated around the steak. Scrape up any additional brown bits if they appear. Simmer the sauce until slightly thickened, about 5 minutes.
Remove from the heat and whisk in 1/2 cup of the blue cheese. Pour the sauce over the steak, and top with the remaining cheese and chives. Serve immediately.
If you can't locate sirloin tips, boneless beef chuck is a good substitute. You can also substitute yellow onions for the shallots.Any high heat, neutral flavored oil will work. See my article on the smoke points of oils and fats for more options.Serving suggestions: Try one of these side dishes alongside the steak!