To make the marinade, whisk together the fish sauce and the next 7 ingredients in a bowl. Place steaks in gallon-sized zip-top bag, pour in the marinade. Squeeze out the air, massage bag a bit to distribute the marinade. Refrigerate for up to overnight.
To make the dipping sauce, whisk together the ingredients in a bowl, or add them to a mason jar, cover and shake.
When ready to cook, preheat grill to 350F-400F (medium-high). Remove steaks from marinade, discard marinade. Grill steaks 6-8 minutes per side, or until desired degree of doneness, turning every 3-5 minutes; remove from grill and cover loosely for 10 minutes. Cut steaks across the grain into thin strips.
Serve with the carrots, red onions, cilantro, mint, cucumber, lime wedges and warmed tortillas.