If the position of elements in the metadata field and the keys of embedded documens is known and then you can use aggregation.

db.foo.aggregate([
  {
    $project : {
      data : {
        "Language" : {
          $arrayElemAt : ["$metadata", 0]
        },
        "City" : {
          $arrayElemAt : ["$metadata", 1]
        },
        "Gender" : {
          $arrayElemAt : ["$metadata", 2]
        }
      }
    }
  },
  {
    $project : {
      metadata : {
        Language : "$data.Language.value",
        City : "$data.City.value",
        Gender : "$data.Gender.value"
      }
    }
  }
])

Result :

{ "_id" : "213412323234", "metadata" : { "Language" : "EN", "City" : "New York", "Gender" : "Male" } }

If any of the above two preconditions mentioned above are not known, you can use mapReduce.

db.foo.mapReduce(function () {
  var key = this._id;
  var metadata = this.metadata;
  var valueEmit = {};
  for (var i = 0; i < metadata.length; i++) {
    valueEmit[metadata[i].id] = metadata[i].value;
  }
  emit(key, valueEmit)
},
function(key, values) {
  // do nothing as it won't be called 
  // for if value is only one 
  // for a key
},
{
  out : {replace : "foobar"}
})

Result :

> db.foobar.find()
{ "_id" : "213412323234", "value" : { "Language" : "EN", "City" : "New York", "Gender" : "Male" } }

Notice that the key has been changed to value instead of metadata. This can be easily fixed using a $project in aggregation on foobar collection.

According to this feature request and its solution, the new feature will be added for this functionality - Function called arrayToObject.

db.foo.aggregate([
  {$project: {
    metadata: {
      $arrayToObject: {
        $map: {
          input: "$metadata",
          as: "pair",
          in: ["$$pair.id", "$$pair.value"]
        }
      }
    }
  }}
])

But at the moment, no solution. I suggest you to change your data structure. As far as I see there are many feature requests labeled as Major but not done for years.

Try this query script

var results = db.meta.aggregate([{
  $project: {
    id: "$_did",
    _id: 0,
    keys: "$metadata.id",
    values: "$metadata.value"
  }
}])

function object(keys, values) {
  var obj = {};
  for (var index in keys) {
    obj[keys[index]] = values[index];
  }
  return obj;
}

results = results.map(function (res) {
  return {
    id: res.id,
    metadata: object(res.keys, res.values)
  }
})