Setting Event handler in DataTemplate inside a custom control

I am trying to build a datagrid where you can filter a column data from a header textbox. I have found some tutorials but they all sound too complicated for what I want to achieve. Furthermore, I want to be able to reuse this FilterDataGrid control in other projects so I thought about creating a custom control.

I think I am pretty close : I can display my textbox in the header while keeping the basic datagrid binding. All I need now is to be able to get the value in my header textbox and use it to filter data in Itemssource.

Here is what I got so far:

FilterDataGrid.cs

using System.Windows;
using System.Windows.Controls;

namespace CustomControlTest
{
    public class FilterDataGrid : DataGrid
    {
        static FilterDataGrid()
        {
            DefaultStyleKeyProperty.OverrideMetadata(typeof(FilterDataGrid), new FrameworkPropertyMetadata(typeof(FilterDataGrid)));
        }

        public void HeaderFilterTextBox_TextChanged(object sender, TextChangedEventArgs e)
        {
            // Filter data source from input text.
        }
    }
}

Generic.xaml

<ResourceDictionary
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="clr-namespace:CustomControlTest">

    <Style TargetType="{x:Type local:FilterDataGrid}" BasedOn="{StaticResource {x:Type DataGrid}}">
        <Style.Resources>
            <Style TargetType="{x:Type DataGridColumnHeader}">
                <Setter Property="ContentTemplate">
                    <Setter.Value>
                        <DataTemplate>
                            <StackPanel>
                                <TextBlock Text="{Binding}"></TextBlock>
                                <TextBox x:Name="HeaderFilterTextBox" TextChanged="HeaderFilterTextBox_TextChanged"></TextBox>
                            </StackPanel>
                        </DataTemplate>
                    </Setter.Value>
                </Setter>
            </Style>
        </Style.Resources>
    </Style>
</ResourceDictionary>

My problem is that I get an error in HeaderFilterTextBox's TextChanged handler :

Error 1 The event 'TextChanged' cannot be specified on a Target tag in a Style. Use an EventSetter instead.

I have no idea how to call this handler in Generic.xaml. If I can do this, the filtering itself should not be too complicated.

Any clue?