Spying on recursive Angular controller method

I have a recursive method that, if a flag is set, will call itself every five seconds. I'm trying to write a test that spies on the method, calls it, waits six seconds and then expects the method to have been called twice. My test fails, as the spy reports the method only being called once (the initial call).

I'm using the Angular style guide, so am attaching these methods to a placeholder for this. I suspect there may be an issue with scoping of the controller returned from angular-mocks $controller(), but I'm not sure—most people are attaching methods to $scope.

Without attaching methods to $scope, how can I create a spy to verify that my method has been called twice?

app.js:

'use strict';

angular
    .module('MyApp', [
        //...
    ]);

angular
    .module('MyApp')
    .controller('MyController', MyController);

MyController.$inject = [
    //...
];

function MyController() {
    var vm = this;

    vm.callMyself = callMyself;
    vm.flag = false;

    function callMyself () {
        console.log('callMyself');
        if (vm.flag) {
            console.log('callMyself & flag');
            setTimeout(vm.callMyself, 5000);
        }
    }
}

appSpec.js:

describe('MyController', function () {

    var $scope;

    beforeEach(function () {
        module('MyApp');
    });

    beforeEach(inject(function($rootScope, $controller) {
        $scope = $rootScope.$new();
        controllerInstance = $controller('MyController', {$scope: $scope});
    }));

    it('should call itself within 6 seconds if flag is true', function (done) {
        controllerInstance.flag = true;
        spyOn(controllerInstance, 'callMyself');
        controllerInstance.callMyself();
        setTimeout(function () {
            expect(controllerInstance.callMyself).toHaveBeenCalledTimes(2);
            done();
        }, 6000);
    }, 7000);
});

Working Plunker