Correctly starting a Task on background thread

Question

I'm trying to properly start a returned Task on a background thread so as not to block the UI thread.

The blocking call is done in another class as such:

var tcs = new TaskCompletionSource<T>();
request.BeginGetResponse(() => DoSomethingSlowThenCompleteTCS(tcs));
return tcs.Task;

I assumed I could simply start the task as such (or a million other variations I've tried:

CallThatReturnsTask()
    .ContinueWith(
        x =>
            Application.Current.Dispatcher.BeginInvoke(DispatcherPriority.Normal,
                new System.Action(() =>
                {
                    // Some continuation stuff that needs to be on the dispatcher
                }
))).Start();

base.OnActivate(); // Call that needs to run immediately

However I've found that I needed to wrap the returning task in a Task.Run() in order to not block the UI thread. I'm almost 100% certain that doing this defeats the purpose of returning the Task in the first place, but it's the only way I've gotten it working.

Task.Run(() =>
    {
        CallThatReturnsTask()
            .ContinueWith(
                x =>
                    Application.Current.Dispatcher.BeginInvoke(DispatcherPriority.Normal,
                        new System.Action(() =>
                        {
                            // Some continuation stuff that needs to be on the dispatcher
                        }
        )));
});

base.OnActivate(); // Call that needs to run immediately

What's the correct way to go about this?

Thanks in advance.

-------------------- Edit 1 --------------------

Is this better? It still seems as if I'm wrapping a task within a task instead of just executing the first task on the correct thread.

Task.Run(() => {
    var result = CallThatReturnsTask().Result;

    Application.Current.Dispatcher.BeginInvoke(DispatcherPriority.Normal, new System.Action(() =>
        {
            // Dispatcher stuff
        }
    ));
});