Preheat the oven to 375 degrees F. Sprinkle the filet generously all over with kosher salt and pepper. Melt
the butter in a medium-sized ovenproof skillet over medium heat until the foam
subsides. Cook the filet until well browned all over, about 3 minutes per side. Transfer the pan to the oven and bake until an instant-read thermometer inserted into the center registers about 130 degrees F, about 10 minutes. Transfer to a cutting board and let rest until room temperature, at least 15 minutes. Thinly slice across the grain.
Stir together the horseradish, mayonnaise
and sour cream
. Spread the bread slices generously with the horseradish mixture and place a slice of beef decoratively on top. Sprinkle with a little sea salt
, and then top with 2 crossed chives
Cook's Note: The beef
can be cooked a day ahead. Slice just before assembling.