Async Singleton

using System;
using System.Threading.Tasks;

namespace TestProject
{
    public class MyClass // cant implement IAsyncInitialization, since 'Initialization' property should be private
    {
        #region Fields

        // 'eagerly initialized'
        private static readonly MyClass _instance = new MyClass ();

        #endregion

        #region Properties

        #region IAsyncInitialization Implementation

        // private instead of public
        private Task Initialization { get; set; }

        #endregion

        #endregion

        #region Constructors

        private MyClass ()
        {
            Initialization = InitializeAsync();
        }

        #endregion

        #region Methods

        /// <summary>
        /// The Singleton instance
        /// </summary>
        public static MyClass Instance()
        {
            // Would this be 'await'ed everytime one calls 'MyClass.Instance()' ?
            // await _instance.Initialization; // It would also change the method to 'public static async Task<MyClass> Instance()'
            return _instance;
        }

        private async Task InitializeAsync()
        {
            // Call async method
            await DoSomethingAsync();

            // Do our own initialization (synchronous or asynchronous).
            await Task.Delay(100);
        }

        private async Task DoSomethingAsync()
        {
            // await Something();
        }

        #endregion

    }
}