How to use Mapbox Geocoding API in JavaScript to reverse geocode a point?

I have read a lot of SO questions and answers and looked at the Mapbox documentation but I can't see a simple example of how to reverse geocode from a latitude/longitude point. The example only shows the URL to use to make a query but presumably there's a way to do it using the MapboxGeocoder object?

So, here, what would I use to display the reverse geocode for lat/long when the user clicks on the map?

var map = new mapboxgl.Map({
  container: document.getElementsByClassName("js-map")[0],
  center: [0, 51],
  style: "mapbox://styles/mapbox/streets-v11",
  zoom: 11
});

map.on("click", function(ev) {
  // 1. Reverse geocode `ev.lngLat.lat` and `ev.lngLat.lng`
  // 2. Do something with the result.
});

You could use the Mapbox SDK for JS which is a wrapper around the rest API.

<script src="https://unpkg.com/@mapbox/mapbox-sdk/umd/mapbox-sdk.min.js"></script>

var mapboxClient = mapboxSdk({ accessToken: mapboxgl.accessToken });
mapboxClient.geocoding
  .reverseGeocode({
    query: "lng,lat"
  })
  .send()
  .then(function(response) {
    if (
      response &&
      response.body &&
      response.body.features &&
      response.body.features.length
    ) {
      var feature = response.body.features[0];
    }
  });

The MapboxGeocoder plugin for Mapbox GL JS is to provide an out of the box search box interface, not for calling the API directly.