Fill a pot with just enough water to cover the potatoes. Add a pinch of salt and boil the potatoes until they are almost tender.
Drain the water and let the potatoes sit in a pot until they are safe to handle. Cut the potatoes in half and set them aside.
Mince the shallots and set them aside for later use when you are ready to make the sauce.
Heat a frying pan over medium-high heat until it is nice and hot. Add the oil. Once the oil begins to smoke slightly, carefully place the steaks in the pan.
After about 3 minutes, reduce the heat to medium and flip the steaks to the other side. Use the flip-often technique by flipping the steaks every two minutes until they reach your desired level of doneness. Ensure that each side is cooked to your liking.
Once done, remove the steaks from the pan, cover them loosely with foil, and let them rest while you make the sauce. (!) Do not wash the pan used for cooking meats. It will be used for making the red wine sauce. To make the red wine sauce, use the same frying pan with all the brown bits remaining in it. Melt approximately one tablespoon of butter over medium to medium-low heat in the pan and add the minced shallots.
Cook the shallots until they become soft, which should take about 2-3 minutes.
Pour in the red wine to deglaze the pan, making sure to scrape up any brown bits from the bottom.
Let the liquid reduce until it reaches a syrupy consistency, which should take about 5 minutes.
Add the beef stock and let it reduce again until it reaches a syrupy consistency, which should take another 5 minutes or so. The sauce should neither be too runny nor too thick.
Remove the sauce from the heat and gradually swirl in the remaining butter, half a tablespoon at a time. Ensure that each bit of butter gets fully incorporated before swirling in more. Once the sauce is shiny and thick, season it with salt and pepper, and set it aside.
Heat the oil over medium-high heat and quickly fry the potatoes, cut side down. Once they develop a nice brown crust, which should take about 5 minutes, season them to taste with salt and pepper and remove from heat.
To plate the dish, smear or drizzle a bit of the red wine sauce on a plate. Place the tenderloin on top, and arrange the fried potatoes, a dollop of pea purée, and pickled Shimeji mushrooms alongside. (!) Make sure to adjust cooking times and temperatures according to your preferred level of doneness for the steaks and potatoes.