I use similar ingredients to the one one the link but a different approach.
Wipe 12oz of mushrooms with a damp paper towel. (I like a mix of white and cremini). Trim the bottoms of the stems if necessary then slice into thirds lengthwise; slice into four slices if large.
Heat a very large sauté pan on the stove over med-high heat. Add a couple tablespoons of evoo or neutral oil and swirl. Melt 1 tablespon unsalted butter into the oil. As soon as the foam subsides add the mushrooms in a single layer - do not crowd. (If the pan is not large enough to do this then do two batches. We're going to do both some browning and some moisture reduction and we need space.)
Once the mushrooms are in the pan, give them a good stir to lightly coat with the fat then spread out.
Meanwhile, mince a shallot or two so that you have about 3-4 tablespoons of minced shallot.
Mince 1 teaspoon thyme leaves, or measure out about 1/2 teaspoon dried.
Cook the mushrooms without disturbing till they release their juices, the juices evaporate and the sides touching the pan brown some (this will boost flavor). Scrape the mushrooms into a bowl. (If you didn't do all the mushrooms at once add a little oil and butter to the pan, then do the same with the next batch. Put them in the bowl with those already done and put the pan back on to heat.)
Add a couple teaspoons of butter to the pan, allow to melt, then add the minced shallot along with a pinch of salt. Cook, stirring constantly, till the soft, about 2 minutes. Add the thyme to the shallot, add the mushrooms from the bowl, stir well to combine and heat well, then immediately add either 3/4 cup cheap white wine, or 3/4 cup red wine (I prefer white here - even for steak), or 3/4 cup lager, or 3/4 cup low-salt chicken stock, or 3/4 cup homemade beef stock. Or make a 3/4 cup blend of wine and stock. (I don't use beef stock here. I'll sometimes use low-salt fresh or canned chicken with the white wine but I do not recommend using canned beef stock - too many off flavors - though you can get away with a mix of 75% chicken and 25% beef if you want to go that route.)
Stir well and bring to a strong simmer. Add a little white pepper. Cook, stirring occasionally, till the liquid in the pan reduces by 3/4. (You can stop at this point, removing the sauce from the heat, and cook the steaks, finishing when the steaks are resting.)
Reduce the heat to very low. (Or, if you cooked earlier, return the sauce to the heat and heat at low.) Whisk in a teaspoon of Dijon mustard. (Optional: whisk in 1/2 teaspoon of Worcestershire, additionally.)
Cook your steaks and rest them on a plate, tented.
Take a stick of cold unsalted butter and slice a 1/2-inch slice off. Stab with a fork. Slide the pan off the heat. Stir the sauce with the butter on the fork, with a somewhat vigorous motion. If the butter comes off the fork re-stab it and continue or simply switch to a whisk. When the butter is melted in and combine immediately repeat with another piece of butter. Do this 4 or 5 more times.
(What you are doing here, with the sauce off the heat and with using the butter on the fork and stirring somewhat vigorously is called 'mounting with butter'. With the sauce only heated to low and then pulled off the heat, the butter should slowly melt. The somewhat vigorous stirring with the butter will emulsify the liquid in the pan with butter, making a very smooth and creamy sauce. The butter must be cold for this to work. If the butter stops melting the sauce has gotten a bit too cold. Simply return the pan to the low heat and continue with the butter. Don't allow the sauce to get too hot, just warm enough to melt the butter gently - so remove the pan again when the butter starts melting well. If this sounds daunting it isn't. Do it once or twice and get used to it and you can do it in your sleep.)
Pour and juices from the resting steaks into the sauce, slice and plate the steaks, give the sauce a quick stir, adjust salt and pepper, spoon over the steaks, sprinkling with minced fresh parsley, if you like; serve.
