1. Make marinade: In a medium bowl or liquid measuring cup, whisk together lime juice, soy sauce, sugar, red-pepper flakes, and oil. Season steaks with salt and pepper; place in a baking dish. Pour 1/4 of marinade over steaks (reserve remaining marinade); turn steaks to coat. Let steaks marinate up to 30 minutes. 2. In a large skillet, cook steaks on medium-high heat, turning once, 2 to 3 minutes per side for medium-rare. Transfer to a cutting board; tent loosely with aluminum foil, and let rest, 5 to 10 minutes. Slice steaks across the grain into 1/4-inch-thick slices; halve slices crosswise. Transfer to a large bowl, and toss with reserved marinade. 3. With a vegetable peeler, cut carrots into long ribbons. Add to steak in bowl, along with lettuce and mint; toss to combine. Divide salad among four shallow bowls. Sprinkle with bean sprouts and peanuts, if desired.