Generously season both sides of the steak with salt and pepper. Don't be afraid to really season it liberally. Set aside and allow to sit at room temperature for about 30 minutes.
Set a large cast iron skillet over medium-high heat with the oil, butter, thyme and garlic. Once very hot, add the steak and cook, without disturbing, for three minutes to develop a nice golden brown sear. Flip over and cook for another 3 minutes on the second side. Using an oven mitt or towel, carefully tilt the pan and use a spoon to baste the steak with the juices for 1 1/2 minutes. Transfer the steak to a plate and set aside to rest for 10 minutes.
Meanwhile, place the bread slices on a baking sheet and brush with the pan juices on both sides. Place under the broiler and toast until golden brown on both sides. Remove from the oven and let cool slightly.
In a small bowl, stir together the mayo, sour cream, as much horseradish as you'd like, chives, and a pinch of salt and pepper.
Slice the steak on a bias and the potatoes into a 1/4-inch slices. To assemble the toasts, spread each piece with a heaping amount of the horseradish sauce. Top with potato slices, steak a pinch of salt and pepper and garnish with fresh chives. Enjoy!