Squeeze two teaspoons juice from one of the lime halves. Put the juice in a bowl and stir in the shallot and a teaspoon of salt. Set aside.
In a large bowl, mix together the garlic, ginger and one tablespoon of the oil. Add the steak and turn to coat. Let stand for 10 minutes.
Heat a lightly oiled gas or charcoal grill to high or heat in an oiled griddle pan over high heat. (On a charcoal grill, most of the coals should be covered with white ash, and you should be able to hold your palm 2.5-5cm above the cooking grate for no more than two to three seconds.)
Brush the cut sides of the remaining lime halves with a total of one and a half teaspoons of oil and season with a generous pinch each of salt and pepper.
Scrape the marinade from the steak and season with one-and-a-quarter teaspoons of salt and half-a-teaspoon of pepper. Grill the steak, turning once, until nicely charred, four to five minutes per side. (Go for 55°C/130°F if you’re using an instant-read thermometer to check doneness.) At the same time, grill the lime halves, cut side down, rotating them occasionally, until charred, about five minutes. Transfer the limes and steak to a cutting board and let rest for 15 minutes.
Stir the remaining two tablespoons oil into the shallot mixture.
Slice the steak crossways into 1cm thick pieces and arrange on a platter. Squeeze the grilled lime wedges over, then spoon the shallot vinaigrette on top. Top with the herbs and chilli.