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Clean and dice the carrots and celery sticks. Chop the garlic cloves and onion and set aside. When using fresh thyme you must rinse and chop them. You can skip this step when using dried thyme.
Heat olive oil in a frying pan and fry the diced carrots, celery sticks, chopped onion and garlic over low heat for about a minute or 10. Add in the tomato paste, thyme and bay leaf. Turn down the heat and let simmer for a while. Cut the mushrooms into quarters.
While the vegetables are cooking, dice the steak and mix with flour, some salt and pepper. You can use a nice big bowl for this. Make sure every piece of meat is coated. Heat a knob of butter in a frying pan and fry the diced meat over high heat.
Keep stirring until the meat turns brown. Transfer the meat to the pan with the vegetables. Pour the wine along with the mushroom stock into the pan and stir frequently to prevent the ingredients from sticking to the pan. Bring to a boil and let simmer for about half an hour.
Heat a big skillet (preferably a cast-iron one) over high heat. Fry the mushrooms without adding any olive oil, butter or grease for about 10 minutes. This method will produce some smoke, but not to worry!
Be sure to stir the mushrooms now and then to prevent them from burning. Transfer the mushrooms to the pan with the meat and vegetables. Let everything continue to simmer for about 15 minutes.
Garnish with chopped parsley or celery leaves. Serve with either mashed potatoes, pasta or rice. Enjoy!