Pat steaks dry and rub liberally with salt. Place in a wide, shallow baking dish and set aside.
In a small bowl, combine the garlic, ginger, brown sugar, soy sauce, fish sauce, and juice and zest of one lime. Stir together, taste and adjust the seasoning, then pour over the steaks, turning to coat the meat in the marinade. Marinate for at least one hour or up to one day.
Remove the steaks from the refrigerator and light the grill (if using charcoal, wait until the coals are glowing and ashy on top; if using gas, preheat to high).
Sear the steaks for 3 to 4 minutes per side, or until a meat thermometer registers 115°F. Remove to a cutting board, cover with foil, and rest the meat for 10-15 minutes (the meat will keep rising in temp to 125, right on the cusp of rare and medium-rare).
While the meat rests, toss the cucumber, radishes, scallions, and herbs together in a medium bowl. Drizzle with olive oil, a pinch of salt, and the juice of the remaining lime.
Slice the meat against the grain and shingle the slices down the center of a large platter. Pile the salad over the meat and serve family-style.