Heat olive oil in a large saucepot over high heat. Add sliced button mushrooms and thyme sprigs; sauté for 5 minutes. Cover with water and bring to a boil. Lower the heat to a simmer and cook for 3 hours.
Strain the stock through a fine mesh strainer, pressing on the mushrooms to release the liquid. Season to taste with salt and pepper. Pour into saucepan and set aside.