public class MyConverter : Freezable, IValueConverter
{
    // Using a DependencyProperty as the backing store for Data.  This enables animation, styling, binding, etc...
    public static readonly DependencyProperty MainContextProperty =
        DependencyProperty.Register(nameof(MainContext), typeof(DependencyObject), typeof(MyConverter),
            new UIPropertyMetadata(null));

    public DependencyObject MainContext
    {
        get => (DependencyObject)GetValue(MainContextProperty);
        set => SetValue(MainContextProperty, value);
    }

    public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
    {
        var window = Window.GetWindow(MainContext);

        throw new NotImplementedException();
    }

    public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture) =>
        throw new NotImplementedException();

    #region Overrides of Freezable

    protected override Freezable CreateInstanceCore() => new MyConverter();

    #endregion
}

<UserControl
    x:Class="WpfApp1.UserControl1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:local="clr-namespace:WpfApp1"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    d:DesignHeight="450"
    d:DesignWidth="800"
    Name="Root"
    mc:Ignorable="d">
    <UserControl.Resources>
        <local:MyConverter x:Key="MyConverter" MainContext="{Binding ElementName=Root}" />
    </UserControl.Resources>
    <Grid Background="{Binding Foo, Mode=OneTime, Converter={StaticResource MyConverter}}" />
</UserControl>