If your steak has a thick fat cap, use a sharp paring knife to score it with a cross hatching pattern. Generously season the steak all over with salt. Let rest at room temperature for 30 minutes or up to 1 hour.
While the steak rests, trim an inch off the ends of the asparagus, then peel the tough, woody bottom two inches off each spear. Cut each spear in half crosswise at an angle.
Heat a large cast-iron or other heavy skillet over medium-high. Dab the steak dry with a paper towel. Add enough olive oil to lightly coat the skillet. Use tongs to hold the steak perpendicular to the cast-iron and gently sear the fat cap until some of the fat renders, about 2 minutes. Carefully lay the steak down and sear on one side without moving it until a nice golden crust forms, about 4 minutes. Flip and sear the other side until browned, about 2 minutes.
Reduce the heat to medium-low. Add the butter, garlic, ginger and thyme. When the butter bubbles, tilt the skillet slightly so the butter pools. Spoon the hot, foaming butter over the steak. Repeat, like you’re bathing it, until the internal temperature of the steak reaches 120 degrees (medium-rare), 3 to 4 minutes. Transfer the steak to a cutting board, season with freshly cracked pepper and let rest for at least 10 minutes or up to 30 minutes.
Meanwhile, raise the heat to medium-high, then add the soy sauce and asparagus to the pan. Cook, stirring occasionally, until the asparagus turns shiny and bright green, 1 to 2 minutes. Turn off the heat and cover with a lid. Let the asparagus steam in the residual heat while the steak rests.
When ready to eat, slice the steak against the grain(perpendicular to the fibers running across the meat), so the meat is especially tender when you eat it. Serve the steak slices sprinkled with salt and spritzed with lime, if using, and with the steamed asparagus.