Heat a skillet over medium high heat. Season generously with olive oil (about 1 tbsp, but how much depends on the size of your skillet) and wait until the olive oil is shimmering. Keep some more oil on hand to put into the pan if it dries up during the cooking process.
Add the mushroom slices to the pan and make sure that they are as evenly spread out as possible. You don't want to overcrowd the pan, so make sure your skillet can fit them all!
Lightly sprinkle some salt around the mushrooms to season them (about 1/8 tsp.) Let the mushrooms sear 1-2 minutes, until golden brown. Flip and let them cook until tender and golden brown all around (you want them to look similar to this picture.)
Add another splash of oil to the pan so that it's not dry. Add the minced shallot. Sauté until golden brown and softened (1-2 minutes.)
Lower the heat to medium. If needed, add a little more oil. If your pan is still seasoned and not dry on the surface don't add anymore! We just want to make sure our garlic doesn't burn on the dry hot pan. Add the garlic and a pinch of salt. Sauté another minute, until the garlic is fragrant. You should see golden browned bits forming at the bottom of the pan from the mushrooms, shallots and garlic. That's what we want!
Pour the 1/2 cup of white wine into the pan. It will be very smoky at first, so stand back to make sure you are as safe as possible! The mixture should be bubbling and those golden browned bits should start to come off of the an and become part of the liquid.
Use a spatula or wooden spoon to scrape the browned bits off of the bottom of the pan, so it becomes picked up by the liquid. This is called "deglazing."
Lower the heat to medium low and let the liquid reduce and lightly bubble for 2 minutes or so, until it looks like the image here.
Add all of the heavy cream.
Mix the heavy cream into the mushroom mixture. Once its fully mixed in, add the butter and continue mixing until melted.
Let the sauce thicken in the pan for about 4 minutes, stirring every 30 seconds or so. It should be lightly bubbling, not extremely boiling. Medium low heat should do the trick, but if its not bubbling at all or thickening, feel free to lightly increase the heat. Taste the mushroom cream mixture and make sure the salt levels are to your liking. If not, add another sprinkle of salt and mix until combined. Once the sauce is thickened, taste it once more to make sure the salt levels are to your liking, then remove it from the heat.
If you want to serve the sauce on another day, let the sauce cool and cover it in an air-tight container. Refrigerate for up to 3 days. If you still have to make the protein or pasta you are serving it with, cover with a lid and then prepare the pasta or protein. You want to make sure it's covered, or else the top will oxidize and develop a film. Covering it ensures that this wont happen! Enjoy!