Preheat the oven to 400 degrees F.
Rub the steak with the olive oil, rosemary, 1 teaspoon salt and 1/4 teaspoon pepper. Let stand at room temperature for 10 minutes.
Meanwhile, stir the sour cream, horseradish, mayonnaise and mustard together in a small bowl; season to taste with salt and pepper.
Heat a large cast-iron skillet over high heat until very hot, about 2 minutes. Add the vegetable oil, swirling to coat. Add the steak and cook until deeply browned on the underside, about 4 minutes.
Turn the steak over and cook another 3 minutes, then transfer to the oven and cook until an instant-read thermometer inserted into the center of the steak registers 120 to 125 degrees F, 5 to 7 minutes. Transfer to a cutting board and let rest for 10 minutes.
Thinly slice the steak against the grain; arrange the slices on the baguette toasts. Sprinkle with finishing salt. Top each crostini with a dollop of the horseradish cream and sprinkle with chives.