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Start by seasoning the steaks on both sides with salt and black pepper to taste. Set aside.
With the back of a knife, lightly crush the whole garlic cloves, set aside as well.
Place a large stainless steel frying pan over medium to high heat. Once hot, add in 2 tbsp of olive oil, the crushed garlic, and the steaks. Cook the steaks for about 1-2 minutes on each side until golden brown.
Transfer the steaks to a plate, reduce the heat to medium low, add in the bay leaf, a couple of sprigs of fresh thyme, and the chilli flakes. Cook for another 2 minutes.
Deglaze the steak pan with the white wine, gently scraping the bottom of the pan with a wooden spoon to release the caramelised bits. Once the alcohol evaporates, stir in the Dijon mustard. Let it reduce for another minute.
Finish the sauce with the cold butter, stirring well to emulsify. Season with more salt and black pepper. Return the steaks to the pan to reheat them for a couple of minutes.
Place a non-stick frying pan over medium heat, add in the remaining olive oil. Fry the eggs until the whites are cooked through but the yolks are still runny. Set aside.
Serve the steaks with a couple of spoons of the sauce, and the fried egg on top. The most common sides you can serve it with are white rice, French fries, and a simple salad. Enjoy!