Preheat the oven to 400 degrees F.
Whisk together horseradish, mustard, garlic, 2 tablespoons black pepper, and 1/4 cup of olive oil in a small bowl. Stir in the panko bread crumbs and set aside. Season the steaks on both sides with coarse sea salt and black pepper. Brush the horseradish bread crumb mixture on 1 side of the sirloin steaks.
In a large saute pan over medium-high heat, add 2 tablespoons of oil and 2 tablespoons of butter. Sear the steaks for 2 minutes, then turn over and cook for an additional 2 minutes. Remove the steaks to a quarter sheet tray with a rack. Drain the excess oil from the saute pan. Put the steaks in the oven and cook until the breading browns, about 15 to 20 minutes. Remove from the oven and let rest.
In the same pan that the steaks were seared, add 2 tablespoons of the butter and the thyme. Turn the heat to high and add the portobello mushrooms. Add the salt and pepper and cook until the mushrooms are soft and slightly colored, about 3 to 4 minutes. Stir in a splash of red wine, the beef broth, and a splash of sherry vinegar. Reduce until the liquid just coats the mushrooms. Stir in the remaining 2 tablespoons of butter to give the mushrooms a creamier consistency. Arrange the steaks on serving plates and top with the mushrooms.
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