Heat olive oil in sauté pan over medium heat. Once hot, add the mushrooms and cook until they are browned and release their liquid, about five to seven minutes. Remove from heat.
Place chopped carrots and onions in a saucepan with 2 cups of water, the soy sauce, pepper, tomato paste, Tabasco and salt. Bring to a boil, reduce the heat, and boil gently for 5 minutes.
Remove carrot-onion mixture from heat and stir in the mushrooms.
After 20 minutes, remove steaks from the oven. They will probably stick to the bottom of the pan so you can incline the pan and pour out most of the accumulated fat. You may need to enlist an assistant in this process since the pan will be hot and heavy.
Spoon the sauce over and around the steaks and place them back in the oven for 15 minutes.
Remove from oven and let cool for a few minutes before serving.