Cut the steaks into strips (5 cm x 2 cm) and transfer to a bowl. Keep them at room temperature — the meat should not be cold when you start browning it. Meanwhile, prepare the other ingredients.
Slice the mushrooms into 3 pieces and set aside. Peel and finely chop the onion and garlic.
Heat a medium-sized pan over medium heat. Once hot, add 1 teaspoon of olive oil and brown the strips of beef in batches. If you add all the meat at once, it will release its juices and steam instead of browning. Use tongs to turn them and brown evenly. These cook really fast so pay attention.
Transfer the browned beef strips to a bowl. Continue browning the remaining beef, adding a bit more olive oil to the pan before each batch.
Lower the heat and add another teaspoon of olive oil to the pan. Add the onion and sauté for about 3 minutes until they soften, scraping the bottom of the pan well. Add the garlic and sauté for another minute to release its fragrance.
Stir in the tomato paste, ketchup and mustard, mixing well. Return the browned beef to the pan, then add the Worcestershire sauce and brandy. Add the mushrooms and mix gently.
Pour in the cream and season with salt and freshly ground black pepper to taste. Stir well and let it cook on medium heat. Once it starts to boil, reduce the heat and cook for another 15 minutes, stirring occasionally, until the sauce thickens.
Turn off the heat and serve immediately.