In a small sauce pot, saute garlic and shallots in olive oil for about 2-3 minutes until shallots begin to become translucent. Pour in mushroom broth and heavy cream and season with salt pepper and fresh thyme. simmer for about 10-15 minutes. Stir in corn starch slurry in the last 3 minutes to thicken up.
While the mushroom cream is simmering. Bring a cast iron skillet to high heat and season both sides of filet mignon with salt and pepper. Place butter in skillet and add in filet. Cook for about 5-6 minutes on each side, occasionally pouring butter over filet with a spoon. Cook until internal temperature is around 135 and take our of skillet and let rest for about 5 minutes.
While filet mignon is resting, add in more butter and sliced mushrooms to the same skillet. Sautee for about 3-5 minutes and take off heat.
To serve, pour about 1/4 cut of mushroom cream onto plate, place filet on top, then add a couple more spoonfuls of the mushroom cream sauce. Top with mushrooms and serve. Enjoy!