Fill a large Dutch oven about 2/3 full with water. Bring water to 130 degrees F (54 degrees C) over medium heat. Attach a candy or oil thermometer to the side of the Dutch oven to monitor temperature.

Generously season steaks with salt and pepper. Heat 1 teaspoon vegetable oil in a large skillet over high heat. Add steaks and quickly sear until just browned, about 1 minute per side. Transfer steaks to a resealable plastic bag, squeeze out all air, and seal.

Place the sealed plastic bag into the Dutch oven, ensuring water temperature remains at 130 degrees F (54 degrees C). Cook for 2 1/2 hours, stirring the bag occasionally.

While the steaks are cooking, heat 1 tablespoon butter in a skillet over medium-low heat. Add mushrooms and cook, stirring occasionally, until soft, about 5 minutes. Transfer to a plate and set aside.

Remove steaks from the plastic bag, reserving any juices. Pat dry and reseason with salt and pepper. Heat remaining 1 teaspoon vegetable oil in a skillet over high heat. Cook steaks to form a crust, about 2 minutes per side. Transfer to a plate.

Add garlic and mushrooms to the skillet, reduce heat to medium, and cook until mushrooms are reheated, about 2 minutes. Stir in reserved steak juices, 2 tablespoons water, and balsamic vinegar.