Preheat a grill pan over medium-high heat or a broiler on high heat. Generously season steak with salt and pepper. Slather with curry paste and oil. Grill or broil steak until medium-rare, flipping once, 3-4 minutes per side. Transfer steak to a cutting board and allow to rest for 5 minutes.
To prepare dressing, in a small bowl, whisk together chile sauce, fish sauce, lime zest and juice, and honey. Set aside.
To serve, slice steak into 1/8” thick strips 3” long. Place steak strips, lettuce, red onion, cucumber, carrot, mint, and cilantro in a large serving bowl and lightly season.