In a small saucepot, saute garlic and shallots in olive oil for about 2 to 3 minutes until shallots begin to become translucent. Pour in broth and heavy cream and season with first amounts of salt and black pepper and the thyme. Simmer for about 10 to 15 minutes. During simmering, mix water and cornstarch until smooth. Stir in cornstarch slurry in the last 3 minutes of simmering time 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 second amounts of salt and black pepper. Place butter in skillet and add in filet. Cook for about 5 to 6 minutes on each side, occasionally pouring butter over filet with a spoon. Cook until internal temperature is around 135°F. and take out 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. Saute for about 10 minutes or until tender. To serve, pour about 1/4 cup of mushroom cream onto plate, place filet on top, then add a couple more spoonfuls of the mushroom cream sauce. Top with sauteed mushrooms and serve. Enjoy!