Provide access to Custom Control Method

Thanks for your response.

What I am trying to do is expose the event handler not listener. In case of your sample, it should be something like this:

In UserControl.Xaml

<UserControl
    x:Class="Usercontrolevent.MyUserControl1"
    xmlns="http://ift.tt/w9rHWX;
    xmlns:x="http://ift.tt/zZkFEV;
    xmlns:local="using:Usercontrolevent"
    xmlns:d="http://ift.tt/PuXO1J;
    xmlns:mc="http://ift.tt/R4RR6u;
    mc:Ignorable="d"
    d:DesignHeight="300"
    d:DesignWidth="400" x:Name="mycontrol">
    
    <Grid>
        <ListView x:Name="listView" ItemTemplate="{Binding ItemTemplate}" ItemsSource="{Binding ItemsSource}"></ListView>
    </Grid>
</UserControl>

In UserControls.cs

public sealed partial class MyUserControl1 : UserControl
    {
        public MyUserControl1()
        {
            this.InitializeComponent();
            this.listView.DataContext=this;
        }
        public static readonly DependencyProperty ItemTemplateProperty =
    DependencyProperty.Register(
    "ItemTemplate",
    typeof(String),
    typeof(MyUserControl1), null
    );
        public DataTemplate  ItemTemplate
        {
            get { return (DataTemplate)GetValue(ItemTemplateProperty); }
            set { SetValue(ItemTemplateProperty, (DataTemplate)value); }
        }
        public static readonly DependencyProperty ItemsSourceProperty =
   DependencyProperty.Register(
   "ItemsSource ",
   typeof(object),
   typeof(MyUserControl1), null
   );
        public object ItemsSource
        {
            get { return (object)GetValue(ItemTemplateProperty); }
            set { SetValue(ItemTemplateProperty, (object)value); }
        }

        public void HandlerIWantToExpose(object sender, RoutedEventArgs e)
        {
            //Do Something
        }
       
    }

In MainPage.Xaml

<Page.Resources>
        
        <CollectionViewSource x:Name="cvs1" />
        <DataTemplate x:Key="AllSubjectsHeaderTemplate">
            <Border BorderBrush="#FF677E7B"
                    BorderThickness="0,0,0,1"
                    Background="#FF534C4C">
                <StackPanel Orientation="Horizontal">
                    <CheckBox x:Name="checkBox"
                              HorizontalAlignment="Left"
                              Margin="10"
                              VerticalAlignment="Top"
                              IsChecked="{Binding IsChecked}"
                              Width="27" Checked="[HandlerExposedByMyUserControl1]" />
                </StackPanel>
            </Border>
        </DataTemplate>
    </Page.Resources>

    <Grid Background="{ThemeResource ApplicationPageBackgroundThemeBrush}">
        <local:MyUserControl1 ItemTemplate="{StaticResource AllSubjectsHeaderTemplate}" ItemsSource="{StaticResource cvs1}"></local:MyUserControl1>
    </Grid>

MainPage.cs

public MainPage()
        {
            this.InitializeComponent();

            ObservableCollection<Test> test = new ObservableCollection<Test>();
            test.Add(new Test { IsChecked = true });
            test.Add(new Test { IsChecked = false });
            test.Add(new Test { IsChecked = true });
            test.Add(new Test { IsChecked = false });
            cvs1.Source = test;

            
        }
    }
    public class Test
    {
        public bool IsChecked { get; set; }
    }