How can I use BrowserMob Proxy with Protractor?

You need to denodeify callbacks, i.e. turn them into Promises so Protractor will wait for them.

Alternative 1: Using already included protractor.promise

  //...
  onPrepare: function() {
    var deferred = protractor.promise.defer();
    proxy.doHAR('http://yahoo.com', function(err, data) {
      if (err) {
        deferred.reject('ERROR: ' + err);
      } else {
        deferred.fulfill(data);
      }
    });
    return deferred.promise;
  }

Alternative 2: Using Q library

var Q = require('q');

  //...
  onPrepare: function() {
    var proxy_doHAR = Q.nfbind(proxy.doHAR);
    return proxy_doHAR('http://yahoo.com');
  }

More info here and here.