Season the steaks generously on both sides with steak seasoning and salt.
For the sauce: add milk and heavy cream to a saucepan over medium low heat bring to a simmer then remove from the heat. Whisk the egg yolks in a bowl with salt and pepper until they turn pale in color. Add a tablespoon of the milk mixture at a time into the egg yolks while gently whisking to temper the yolks (so they don't curdle and cook). Once about half of the milk mixture has been incorporated stir the yolk mixture back into the saucepan. Stir in the mustard. Place back on medium low heat while stirring until it becomes smooth and thick (do not let it come to a simmer or it will break). Then remove from the heat immediately and set aside in a bowl. Stir in the parsely and season with salt and pepper to taste. Add more mustard if needed. Let cool, stir occasionally.
Preheat a cast iron skillet or heavy bottom non-stick pan over medium heat. Once hot, add the oil and mushrooms. Gently saute until golden brown and somewhat crispy. Season with salt then remove from the pan and set aside.
Place the steak into the pan and sear well on all sides to get a nice char.
Add in the butter, garlic, and thyme.
Continue cooking the steaks while using a spoon to baste them over the top with the butter until they reach your desired temperature using a thermometer (see below). If desiring more than medium doneness it is recommended to finish the steak in a 350°F oven so that the outside doesn't burn.
Remove the steak from the heat and allow to rest for 5 minutes before serving with mushrooms and crusty bread. Serve with mustard anglaise.