Pat the beef medallions dry with paper towels and season both sides generously with salt and black pepper.
Heat a heavy-bottomed skillet over medium-high heat with the oil and 20g of butter.
Once the butter is foaming, place the medallions in the pan and sear for 3 to 4 minutes per side for medium-rare.
Remove the beef from the skillet and set aside on a warm plate to rest under foil.
In the same skillet, add the remaining 20g of butter and the mushrooms; sauté until golden brown and the moisture has evaporated.
Add the minced shallots and cook for 1 minute until translucent.
Deglaze the pan with the Cognac, scraping the bottom with a wooden spoon to release the fond.
Pour in the heavy cream and simmer over medium heat for 3 to 5 minutes until the sauce coats the back of a spoon.
Return the medallions and any accumulated resting juices to the skillet to reheat for 1 minute.
Taste and adjust seasoning of the sauce, garnish with chopped parsley, and serve immediately.