Heat 1 tablespoon of the olive oil in a medium pan over medium-high heat. Add the mushrooms to the pan, lightly season with salt and pepper, and cook for 5 minutes, stirring. Remove the mushrooms from the pan and set aside. Add the additional 1 tablespoon of olive oil to the pan, following with the shallots and thyme. Season with salt and pepper and cook until the shallots are soft, approximately 5 minutes, stirring. Remove from the pan and set aside.